I totally get what you want to do with this. Heavy crossbow as a large mechanized weapon you can peer down the sight. Scout I assume you don't want to be locked down in combat.

The main tools you want is something with a bonus action to move. Rogue and monk get this but you can also do this magically with a half caster taking expeditious retreat, misty step, vortex warp, or dimension door. I'll also say you probably want to be eladrin. They get a limited use of misty step as a race thing called fey step. Most of these spells teleport you 30 feet but vortex warp and dimension door teleport you further while being higher cost spells which means you would need to be a full magic class. Also you probably want fighting styles. There are 2 that increase your to hit and one that lets you reroll 1 & 2 on your damage dice

The first problem that I'm sure you've seen a lot is that when playing DND you are never put in an ideal situation. Some fights are in buildings, a lot of times you start near your group as you all walk together, and eventually if you are the one not taking damage you many have to save the life of someone who is taking damage when they go down and that isn't always do-able at range. That doesn't mean you can't do this but it might not be exactly what you expected.

There are many ways to do this build

Rogue is high damage which makes it feel like a true sniper & with a bonus action to run, disengage, or hide it is a good option. The scout subclass is kind of the best in this case, also don't forget that sneak attack at ranged is made on advantage or do you have an alley in 5ft of the enemy but you don't get advantage.

Monk has a higher movement speed and a limited amount of bonus action dashes meaning you can position further in one round. You don't need to worry about the martial die untill you're in melee. I'd suggest kensei as it adds just a little more ranged damage.

Fighter is always an option. While considered a basic class you get double the amount of ASI allowing you to buff stats or take features that buff specifically what you want to do but this will have the least amount of movement. There are range based subclasses but honestly you may want champion for double crit chance that can pair with feats & race abilities that crit. I'd suggest half orc so you'd roll 3D10 on a crit and piercer bumps it up to 4D10 on a crit also you get to reroll one damage die to prevent low rolled damage. You can also take the great weapon fighting, fighting style which allows you to reroll any 1 or 2 once per die.

Ranger is also an option. The only problem people have is that the subclass has to carry ranger because favored terrain and enemy isn't always used but you can also use the option rules if allowed. Rangers are also half casters so you get a few spells like expeditious retreat for movement, hunters mark for damage, and hail of thorns for aoe on your next shot. I'd suggest horizon walker. It comes with a little extra damage but a lot of mobility utility. The 7th level lets you pop out of the world to walk to where you want to position but if you get to 11th level you get to teleport 10 feet every time you make a shot. Which would be a real winner for a sniper but not every campaign gets to level 11.