The initiative effectively determines how surprised the creature is
If we consider only the rogue and the orc, there are two possible cases: either the orc's initiative is higher, or the rogue's is. If the orc's initiative is higher, they are still surprised and unable to act on their first turn, which means that the rogue gets to act first, but after the rogue acts, the orc reacts quickly to the surprise attack and gets to act on their next turn before the rogue's 2nd turn. If the rogue's initiative is higher, the rogue still gets to act first, but in addition, the orc is so caught off guard that the rogue has time to act again on their 2nd turn before the orc can react at all.
So, comparing the two cases, we can see that the rogue always gets to act first, because the rogue has surprised the orc. So the initiative roll isn't determining who acts first, but rather determining whether or not the ambush is so effective as to grant the rogue an extra turn before the orc can respond.
When we add in the rogue's assassinate feature, things get a bit more complicated, but once again, the same general principle applies: initiative determines how surprised the orc is. If the rogue wins initiative, the orc is caught completely with their guard down and the rogue is able to use their assassinate feature, because their first turn comes before the orc's first turn. If the orc's initiative is higher, then despite being ambushed, the orc is somehow more prepared for the attack, and the rogue can't use their assassinate feature.1
The rules don't explain how or why there is a difference here, so it's up to the DM to make up an explanation within the fiction to justify the mechanics. For example, the DM could say that as the rogue attempts to quietly dash up behind the orc and slit their throat, the orc hears a pebble that the rogue accidentally kicked across the floor as they ran, and just barely has time to turn around and face the rogue as their first attack lands. Or perhaps the orc is a guard who is constantly scanning the room, and they just happened to look in the rogue's direction at the last second. In these cases, the rogue still gets the element of surprise and the first strike, but they don't get the benefit of catching the orc completely unaware.
1 The rules are ambiguous about precisely when surprise ends. If the DM rules that creatures remain surprised until the end of the first round rather than the end of their first turn, the auto-crit feature of Assassinate would still be usable, but not the advantage on the attack.