The Gym wiki page has the requirements in the Levelups section. See here: https://summoned-by-accident.fandom.com/wiki/Gym#Levelups
I just tried on the public build up above and it worked fine.
I met Trald in the Morning/Afternoon at the Gym so I know him. Then I fought the Drunk Wolf at night. I sold stuff to Zorro so I had money for the Gym membership. Then I went to the Gym in the Afternoon while Gen is at the front desk, paid in to the Gym, and then picked the option for Trald working out in there.