Hand crossbow fighter.

Variant Human, point buy 15 dex 15 con and whatever for the rest, add +1 to dex and +1 to con from human. Choose skills and archetype as you feel, but take archery for your fighting style at level 1, crossbow expert as your free human feat, and start with at least one hand crossbow (fighter starts with two martial weapons).

You can now fire your hand crossbow and then use bonus action to fire it again. +7 to hit each shot (+3 dex +2 archery +2 dex) and +3 damage. Not bad for first level.

Get whatever archetype.

At level four grab sharpshooter and at level five you get a bonus attack. You can now take -5 to hit for +10 damage. You're attacking at +8 (+3 proficiency now) and that goes to +3, but your average damage per hit goes from 6.5 to 16.5. It's an increase in average damage per turn if you're firing at AC 20 or lower (ie all enemies at level 5). Against AC 15 you go from 13.65 to 22.275 average damage per turn by using sharpshooter on all three attacks (two normal and one bonus).

RAW basically require that you do this with a hand crossbow in one hand and the other hand empty. You can't use a shield or a sword in one hand or anything cause you need to reload. But you can fight in melee without disadvantage so who cares, because you're doing 20+ freaking damage per turn.

I recommend grouping with high str characters as they can carry more spare bolts for you to use when you run out because you're a freaking machine gun.

Re: archetype. Champion is a slight damage increase. Battlemaster is a damage decrease because you're already action starved, but it gives you utility beyond pincusioning foes and maybe makes your party hate you like 4% less. Never tried Eldritch Knight but could be fun?