There are plenty of ways to narrate this scenario, with some environmental factor giving anyone that gets to act before the sniper that something is up (snapping twig, rustling in the bushes, faint smell of gun oil, light reflecting off a lense or barrel, etc)

Exactly. How many Westerns do we have a bad guy about to ambush our hero, there's a close up on Clint's eyes shifting to the side as they catch sight of . . . something, and he whirls and guns down the enemy out of the barn. Keenly aware badass action heroes are keenly aware enough to have spider sense when it comes to these things.

I would have the sniper roll their hide against one of the players (go with the highest vigilance), and then roll the initiative as normal with some blues or blacks applied depending on how the vigilance comes out.

I like taking care of as much as possible with a single roll of the dice. I also like my approach of adding Difficulty to the roll for the adverse conditions like ambush or environmentals (fog, smoke, bustling crowds, etc). It makes the whole thing cleaner I think, and it provides a more compelling reason for everyone to be interested in putting some effort into raising initiative skills. They went to the trouble of creating this multi skill/stat system for initiative and then really didn't put much into the need to go beyond simply rolling your 3 greens for stat X. It adds depth and challenge to initiative I think and makes it less bookkeepey and clunky. Since they really don't provide much direction for ambush/surprise, it falls to GMs largely I think. Just my personal tastes.

A decent side bar in the core books on reasons to add Boost, Difficulty and Setback to Initiative checks would have gone a long way to improving this situation. I truely believe this is the intended way of running an ambush situation, but they left it slightly too vague.

Perhaps Endless Vigil or No Disintegrations will have some chapter 3 ideas on running an Ambush, or the Warrior book when that comes out.

Would you guys allow a single NPC vs a single PC for an intiative check even if they are in a group if the NPC is only after the one PC?

Last session shortly after a combat encounter began I had a 1 NPC vs 1 PC cool check quick draw show down, it was epic. But that's about the only situation where I would answer "yes" to your question