24 hours

So somehow, based on a nuclear test going off, within 24 hours, you have these objects, whatever they are, appearing in geosynchronous orbit.

And how can they be so close that in 24 hours they're able to be here?

If it was the bomb casing, just let's say some bit of it survived, it's not going to sit in one place in the sky for 24 hours to be seen as a transient afterwards.