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.
I'm still traumatized from the crit fail I rolled during a campaign five years ago.
I was playing a gunslinger, and made an admittedly foolish attempt to shoot a vermin crawling near my foot. I rolled a 1, and the DM ruled that meant I shot myself in the foot. I couldn't really argue with that outcome, but it was hard to come back from that. It was a harsh post-apocalyptic setting, which meant that the other characters were obliged to rib me for it incessantly, and my character could never seem to redeem himself afterwards.