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###There is enough time for the target to notice you between actions, and in combat they probably will.

###Misty Step has a verbal component. The first issue is that Misty Step has a verbal component. So you need to make sure that the creature can't hear you casting it to remain hidden. But, I'm going to assume you can take care of that issue, as there are many ways around it (sorcerer metamagic for example).

###In combat, enemies typically have 360 degree awareness The main problem for you is that 5e doesn't have default facing rules. As described in the quote: enemies in combat stay alert for signs of danger all over. If you teleport into plain view during combat, it's well within the DMs purview, and arguably true to the rules, that the creature will see you since the creature is looking all over for signs of danger. Especially if you are making any kind of noise.

###Out of combat you have a bit more of a shot at this working As the rules note, creature are only alert for signs of danger all around during combat. Additionally, the DM might allow you to stay hidden if you approach a creature who is distracted by something. So, if you teleport behind a distracted creature outside of combat, the DM could rule quite reasonably that you begin combat by attacking from hiding because your target is distracted.

###If you do remain unnoticed before combat starts, you will likely surprise your enemy The DM determines who is surprised. As noted on page 189 of the PHB:

##There are some optional facing rules that make this rely less on DM fiat The default rules give the DM room to rule that a creature can be distracted enough to not see you in combat, but it is not a guarantee. It depends on what the DM thinks of the situation. However, page 252 of the DMG provides rules for proper creature facing. If you are using these rules, there is a cone of space behind most creatures (their backside) that they can't see in. So, if you teleport into that space, you are unseen at that point. In this case, it's pretty clear that you will have advantage on your attack and might surprise creatures at the start of combat if the DM rules that your target doesn't notice you.

There is enough time for the target to notice you between actions, and in combat they probably will.

Misty Step has a verbal component.

The first issue is that Misty Step has a verbal component. So you need to make sure that the creature can't hear you casting it to remain hidden. But, I'm going to assume you can take care of that issue, as there are many ways around it (sorcerer metamagic for example).

In combat, enemies typically have 360 degree awareness

The main problem for you is that 5e doesn't have default facing rules. As described in the quote: enemies in combat stay alert for signs of danger all over. If you teleport into plain view during combat, it's well within the DMs purview, and arguably true to the rules, that the creature will see you since the creature is looking all over for signs of danger. Especially if you are making any kind of noise.

Out of combat you have a bit more of a shot at this working

As the rules note, creature are only alert for signs of danger all around during combat. Additionally, the DM might allow you to stay hidden if you approach a creature who is distracted by something. So, if you teleport behind a distracted creature outside of combat, the DM could rule quite reasonably that you begin combat by attacking from hiding because your target is distracted.

If you do remain unnoticed before combat starts, you will likely surprise your enemy

The DM determines who is surprised. As noted on page 189 of the PHB:

There are some optional facing rules that make this rely less on DM fiat

The default rules give the DM room to rule that a creature can be distracted enough to not see you in combat, but it is not a guarantee. It depends on what the DM thinks of the situation. However, page 252 of the DMG provides rules for proper creature facing. If you are using these rules, there is a cone of space behind most creatures (their backside) that they can't see in. So, if you teleport into that space, you are unseen at that point. In this case, it's pretty clear that you will have advantage on your attack and might surprise creatures at the start of combat if the DM rules that your target doesn't notice you.

##There is enough time for the target to notice you between actions, and in combat they probably will.

The first issue is that Misty Step has a verbal component. So you need to make sure that the creature can't hear you casting it to remain hidden. But, I'm going to assume you can take care of that issue.

The main problem for you is that 5e doesn't have default facing rules. Enemies are treated as being aware of everything in plain view around them at all times in combat. Surprise doesn't affect this. All surprise does is basically force a surprised creature to skip their first turn in combat. If you teleport into plain view to make your attack before combat starts, there are a few ways I foresee this could turn out:

1. The DM lets you "attack from behind" you surprise them and are an unseen attacker. It's within their right to do so, but this isn't strictly RAW how combat works (Unless you are using the optional facing rules in the DMG)

2. The DM calls for everyone to roll initiative once you declare your intention to attack. Combat starts, with or without surprise at the DMs discretion, and then you are plainly visible so you are not an unseen attacker. This is probably the closest ruling to RAW.

3. The DM calls for initiative, but allows you to remain hidden so you still get to be unseen, regardless of if you surprised the target or not. Again, this is within their right to do so, but it's flexing the rules a little bit to give you some pay off.

The only way to know for sure which ruling your DM will follow is to ask them yourself, but as far as rules as written go, option 2 is what you should expect by default.

##If you try this after combat starts, it won't work at all.

If you teleport into melee range after combat starts, you are in plain view the instant you arrive, and so are not unseen when you make your melee attack unless you are invisible or the target is blind.

##What about those optional facing rules?

There are optional rules in the DMG that do describe more realistic facing. If you are using these rules, there is a cone of space behind most creatures (their backside) that they can't see in. So, if you teleport into that space, you are unseen at that point. If you are using these rules instead of the default assumption, then what you are trying to do should work well in and out of combat. You will have advantage on your attack and might surprise creatures at the start of combat if the DM rules that your target doesn't notice you when combat begins.

Tl;dr - Without variant rules, you may or may not be noticed. It depends on your DM ruling the situation in your favor. If you use some variant rules though, you probably won't be noticed.

###There is enough time for the target to notice you between actions, and in combat they probably will.

First of all, let's review the relevant rules on page 177 of the PHB on hiding:

You can't hide from a creature that can see you, and if you make noise (such as shouting a warning or knocking over a vase), you give away your position... In combat, most creature stay alert for signs of danger all around, so if you come out of hiding and approach a creature, it usually sees you. However, under certain circumstances, the Dungeon master might allow you to stay hidden as you approach a creature that is distracted, allowing you to gain advantage on an attack before you are seen.

Based on those rules, you will need to remain unseen and unheard for this to even have a chance at working. Let's assume that you have already tried to hide in cover before trying this out.

###Misty Step has a verbal component. The first issue is that Misty Step has a verbal component. So you need to make sure that the creature can't hear you casting it to remain hidden. But, I'm going to assume you can take care of that issue, as there are many ways around it (sorcerer metamagic for example).

###In combat, enemies typically have 360 degree awareness The main problem for you is that 5e doesn't have default facing rules. As described in the quote: enemies in combat stay alert for signs of danger all over. If you teleport into plain view during combat, it's well within the DMs purview, and arguably true to the rules, that the creature will see you since the creature is looking all over for signs of danger. Especially if you are making any kind of noise.

###Out of combat you have a bit more of a shot at this working As the rules note, creature are only alert for signs of danger all around during combat. Additionally, the DM might allow you to stay hidden if you approach a creature who is distracted by something. So, if you teleport behind a distracted creature outside of combat, the DM could rule quite reasonably that you begin combat by attacking from hiding because your target is distracted.

###If you do remain unnoticed before combat starts, you will likely surprise your enemy The DM determines who is surprised. As noted on page 189 of the PHB:

The DM compares the Dexterity (Stealth) checks of anyone hiding withe the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn't notice a threat is surprised at the start of the encounter.

So, if you teleport behind a creature, and your DM ruled that you didn't immediately reveal yourself, and your target didn't notice you, and you make your attack, you would surprise that creature. Keep in mind though that surprise is only determined at the start of each encounter. So, if you teleport into a fight in progress, you cannot surprise anybody anymore.

##There are some optional facing rules that make this rely less on DM fiat The default rules give the DM room to rule that a creature can be distracted enough to not see you in combat, but it is not a guarantee. It depends on what the DM thinks of the situation. However, page 252 of the DMG provides rules for proper creature facing. If you are using these rules, there is a cone of space behind most creatures (their backside) that they can't see in. So, if you teleport into that space, you are unseen at that point. In this case, it's pretty clear that you will have advantage on your attack and might surprise creatures at the start of combat if the DM rules that your target doesn't notice you.

##There is enough time for the target to notice you between actions, and in combat they probably will.

The first issue is that Misty Step has a verbal component. So you need to make sure that the creature can't hear you casting it to remain hidden. But, I'm going to assume you can take care of that issue.

The main problem for you is that 5e doesn't have default facing rules. Enemies are treated as being aware of everything in plain view around them at all times in combat. Surprise doesn't affect this. All surprise does is basically force a surprised creature to skip their first turn in combat. If you teleport into plain view to make your attack before combat starts, there are a few ways I foresee this could turn out:

1. The DM lets you "attack from behind" you surprise them and are an unseen attacker. It's within their right to do so, but this isn't strictly RAW how combat works (Unless you are using the optional facing rules in the DMG)

2. The DM calls for everyone to roll initiative once you declare your intention to attack. Combat starts, with or without surprise at the DMs discretion, and then you are plainly visible so you are not an unseen attacker. This is probably the closest ruling to RAW.

3. The DM calls for initiative, but allows you to remain hidden so you still get to be unseen, regardless of if you surprised the target or not. Again, this is within their right to do so, but it's flexing the rules a little bit to give you some pay off.

The only way to know for sure which ruling your DM will follow is to ask them yourself, but as far as rules as written go, option 2 is what you should expect by default.

##If you try this after combat starts, it won't work at all.

If you teleport into melee range after combat starts, you are in plain view the instant you arrive, and so are not unseen when you make your melee attack unless you are invisible or the target is blind.

##What about those optional facing rules?

There are optional rules in the DMG that do describe more realistic facing. If you are using these rules, there is a cone of space behind most creatures (their backside) that they can't see in. So, if you teleport into that space, you are unseen at that point. If you are using these rules instead of the default assumption, they what you are trying to do should work well in and out of combat. You will have advantage on your attack and might surprise creatures at the start of combat if the DM rules that your target doesn't notice you when combat begins.

##There is enough time for the target to notice you between actions, and in combat they probably will.

The first issue is that Misty Step has a verbal component. So you need to make sure that the creature can't hear you casting it to remain hidden. But, I'm going to assume you can take care of that issue.

The main problem for you is that 5e doesn't have default facing rules. Enemies are treated as being aware of everything in plain view around them at all times in combat. Surprise doesn't affect this. All surprise does is basically force a surprised creature to skip their first turn in combat. If you teleport into plain view to make your attack before combat starts, there are a few ways I foresee this could turn out:

1. The DM lets you "attack from behind" you surprise them and are an unseen attacker. It's within their right to do so, but this isn't strictly RAW how combat works (Unless you are using the optional facing rules in the DMG)

2. The DM calls for everyone to roll initiative once you declare your intention to attack. Combat starts, with or without surprise at the DMs discretion, and then you are plainly visible so you are not an unseen attacker. This is probably the closest ruling to RAW.

3. The DM calls for initiative, but allows you to remain hidden so you still get to be unseen, regardless of if you surprised the target or not. Again, this is within their right to do so, but it's flexing the rules a little bit to give you some pay off.

The only way to know for sure which ruling your DM will follow is to ask them yourself, but as far as rules as written go, option 2 is what you should expect by default.

##If you try this after combat starts, it won't work at all.

If you teleport into melee range after combat starts, you are in plain view the instant you arrive, and so are not unseen when you make your melee attack unless you are invisible or the target is blind.

##What about those optional facing rules?

There are optional rules in the DMG that do describe more realistic facing. If you are using these rules, there is a cone of space behind most creatures (their backside) that they can't see in. So, if you teleport into that space, you are unseen at that point. If you are using these rules instead of the default assumption, then what you are trying to do should work well in and out of combat. You will have advantage on your attack and might surprise creatures at the start of combat if the DM rules that your target doesn't notice you when combat begins.