It's 2 am. What good "could" happen?

The title perplexed me, so I listened to the lyrics. It describes being awake around 3:35am and in a weird state.

Db. Post

Heh! I’m in a weird state every 2am.

Arkansas

My alarm goes off, because someone’s gotta get up to make the donuts…Happy Thanksgiving!

In my younger days getting a late night meal with my friends after a night of drinking was always pretty good.

Ours spring forward at 1 AM.

It once took me an hour to walk up one flight of stairs: 12:59 at the bottom, 2:00 at the top.

Re the question in the OP: not much, except continuing to sleep. I know from personal experience that any phone call between 10 PM and 8 AM bears Very Bad News.

Historically I think it was “Nothing good happens after midnight”.

At the time, my mother amended this to 8 PM. Children could be gone all day doing golly knows what, but there was no quarter given for being outside past 8 PM. Dark actually, about the time the streetlights came on.