Firstly, use Passive Perception.
Have your assassin hidden at the outset, and use the players' Passive Perception scores to determine if anyone was aware of him or not. This reduces rolling, or meta-actions by the players after asking them to roll. I'd recommend having your assassin roll for his Stealth, instead of setting an arbitrary DC, to prevent you from planning around your PCs' strengths inadvertently.
If you want to be very sure your assassin has a good chance to be hidden and not detected, and a good chance to hide for his getaway, consider giving him Expertise in Stealth, or a similar good bonus, which is in line with what a Rogue with Assassin archetype would get.
Additionally, suggested by Meta4ic in the comments:
Another way to increase your assassin's chances is to grant him advantage on his stealth check. I allow it for players when then take special measures (cover their face with soot, create a diversion, etc.), so it seems fair to me to allow the same for a NPC.
Secondly, use the Surprise rules, as mentioned in THiebert's answer.
On PHB p. 189 the surprise rules are outlined:
The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with 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.
If you’re surprised, you can’t move or take an action on your first turn of the combat, and you can’t take a reaction until that turn ends. A member of a group can be surprised even if the other members aren’t.
This gives your assassin a full round of action to spring on the players, and get a head start on his getaway. This also denies the players actions or reactions until their turn ends. You can either use a direct Perception roll upon ambush, or, as I've already outlined, Passive Perception, reducing the number of rolls.
If you're following what I've said, the players should only have had to roll initiative so far. Note that Passive (or Active) Perception combined with the Initiative roll is still letting your PC's abilities work for them (or against them). Keep in mind, some PCs may not be surprised, so account for that in your narrative, and accept this may get your assassin caught - have something ready if this happens.
(Optional) Give your assassin a Bonus Action Hide ability.
This is in line with the Rogue's Cunning Action and the actual Assassin archetype. This also allows him to hide the turn he fires, while the PCs are still surprised, and then use his movement that turn to get a head start. On subsequent turns, consider letting him use a Bonus Action Dash, again consistent with Cunning Action, and giving him a good chance of getting away.
Note: if you let him hide in this way (or in general really, for quicker play and less rolls), make his attempt against the players' Passive Perception, and make them take a Search action on their turn if he beats their Passive and they want to try finding him.
Finally, if they do give chase or initiate combat, follow the relevant rules, and do not fudge anything.
Chase rules are on DMG p. 253, and the combat rules should be well known.
If you can't afford to let your assassin get caught because it messes with your story, you may need to rethink your story somewhat. The players should be rewarded if they are able to catch the would be assassin. Information, a plot hook, or at the very least, with preventing the assassin from trailing them for another attempt, reporting back to whoever ordered the hit, or potentially with a new ally if they're persuasive enough and the assassin is open to that.
However, if you're following the suggestions I've given, with a high Stealth score, bonus action Hide and Dash actions, and you properly surprise the PCs, you should have a very good chance of the hit and run with minimal dice rolls you were looking for. At this point, the players should only have made one dice roll (initiative), and maybe an active Search check if he managed to hide successfully.
Bonus Action Dash should also let him cover a lot of ground, meaning the PCs will have to work hard to catch your assassin. If they do, they deserve it and any reward that comes as a result. Also since these abilities are consistent with PCs, if he does escape, they shouldn't feel cheated, or that you gave him arbitrary abilities to DM Fiat his getaway. Additionally, you gave them full agency to react as they see fit. Failing skill checks, or not having the specific tools to catch him in that moment is not stripping them of their agency.
Final Additional Note: Under no circumstances should you try to work around, or negate a feat choice such as Alert or Observant.
PCs give up an ASI, and a wide choice of other potential Feats that may be better value in combat, just so they can be good in this specific circumstance. Working around that cheats them of their character choice.