From what I understand, you must have a pet of the same or higher level already before you can uncage one.
I believe you can, say, grab 3 level 1 pets and use them to capture level 4 pets,
then take those 3 level 4 pets and use them to capture level 8 pets,
then use those 3 level 8 pets to capture level 12 pets, etc and try to hop up the level scale that way.
But the highest level you wind up with through level jumping is 22, I believe,
because the capture of a level 24 pet makes it lose 2 levels because of the trauma of being caught, lol.
Then, just level one of those 22s up to 25, then you can uncage level 25s.
Hopefully this makes sense to someone other than me, haha, and I hope that helps.