If your character's starting off at level one, they're really only getting started with adventuring. You can let that be reflected in their backstory.
If you want to play a badass, starting above level 1 is allowed, though probably not recommended for new players still learning the rules of whatever system you're playing.
Not OP but sure!
Consider that a level 1 commoner is like... well, let's just say the average American. Not your average gaming enthusiast, of course, but like, one of those folks working down at Wendy's, who probably weighs a little extra and won't take shit from you if you try an' start somethin'. Can probably run a mile in 15 minutes, or 20 minutes if they're in heels, but make that 12 minutes if cops are involved.
Speaking of cops, I feel like they're a pretty fair baseline of what a level 1 fighter would be. You know the type: usually a bit overweight, but they'll still run you down, and you can bet your sweet bippy they know how to use their guns. Some of the sneakier roguish types can evade them, but they do travel in pairs because hell if they're gonna take any chances against the action economy in this world.
Consider then that coming out of basic training, the average male needs to pass a test during which they must be able to perform, in sequence, ~40 pushups in 2 minutes, ~50 sit-ups in 2 minutes, and then run two miles in under 17 minutes, pretty much back to back.
This is in addition to actual skills learned. While most civilians can go to a shooting range and hit a target with a gun pretty well given half an hour of safety training, by comparison, basic training involves multiple hours per day of gun training for 6-8 weeks.
This is for army basic training, your basic-bitch grunt shooty boys, this isn't even the elite marine training or anything which would almost certainly be even higher levels of fighter!