How to properly deal with your very first big fuck up?

Admit it, communicate the issue and get the team working on it, if you have one.

But another point: In my field, if you’ve never brought down production or caused an outage, you probably aren’t doing much — and nothing useful. In IT sysadmin/operations you’re touching live stuff nearly all of the time. Unlike developers, we don’t have test environments because there are some things in infrastructure you simply cannot duplicate to even do a test.

So you’re not much of a sysadmin if you’ve never caused an outage. And I would not trust you because it means you have no experience no matter what your title might say.