Ahhh, you've found rule #1 of putting the dash back in... always test the glove box before screwing it back in!!
Getting it open again will be a PITA, and to be honest I can't actually remember how I opened one last time as after doing it once, I always triple check the catch before putting the final screws in.
I'm trying to think, but you may have luck accessing the catch either from the center of the dash, with the fascia removed, or possibly from unbolt ingredients the bottom of glove box, and with the lower trim panel removed, being able to reach up around the glove box unit to trip the catch.
There's also a blanking plug on the side of the dash top, but again, not sure if removing that will give enough access for the likes of a piece of wire with a hook on it to reach the catch.
Hope you manage to get it open, let us know how you did it too!
'06 4.2 Supercharged Black/Cream "Jess" -- Bought April 2021 (NZ)
'01 4.6 Vogue Black/Lightstone "Snog" -- Bought Jan 2012
'99 4.6 HSE Cobar Blue/Lightstone -- Sold March 2009
'95 4.6 HSE Epsom Green/Tan -- Traded June 2008