Q&A

It will go into gear with the engine off and when the clutch is depressed, it will move slightly in the beginning, after it is warmed up for ten minutes or longer, it will shift but not super easy, after a little driving it shifts just fine

Here is what i would do,drain and refill trans. with proper lube. If that doesn't help replace clutch slave cylinder!
Been there done that! In fact the slave cyl. might be the first thing to try. Fixed a Nissan that was doing the exact thing.
Bet if you pumped the clutch a bunch of times it would be ok even cold. Is is not the clutch master cyl but the slave cyl.