Not sure you can without the possibility of damage.
From your description, likely the outer knob has broken free from the inner mechanism shaft. Is the Latch Keyed (lockable) or is it just a latch release knob?
Is this the Dash Glovebox or a Center Console Glovebox?
Is the inner glovebox cardboard or plastic? You could tunnel through from underneath, remove contents and release the latch, then repair or replace the inner box.
You might be able to pry the outer button off with two screwdrivers wraped in electric tape to not scratch the glovebox door.
You might be able to sneak a thin, flexible blade between the glovebox door to access the latch release.
Do you know what the latch mechanism in question looks like?
It isn't Fort Knox, but trying to force it may well damage something, but that might be the best you can do.
Worst case, a Locksmith?