Usually one can slide the female onto the male about 1/4 - 1/2" before pressing the button down (I put WD-40 or equivalent on that button). With the button down, slide it on the rest of the way (I don't use grease as it seems to build up with dust and grime over time with grease for me anyway). I spray some WD-40 on the both before assembling. Also, protect the PTO end from being on the ground and catching a lot of water while the attachment is stored, if outside. If there is grease/dirt/grime on the connections, spray with Brake cleaner to clean them up well before trying to slide them together. Get any new paint off if possible. Some tractors come with paint on the male PTO end, and it takes up needed space/tolerance. Clean and dry is the best. No grease on the hands and not slippery to handle.
Some PTO connections have a twist ring that locks/unlocks. Keep these clean as well.
But likely most of us have similar frustrations being in an awkward, hard-to-reach from a difficult position to stand while connecting the PTO. Sometimes they go together real easy, and other times it seems to be a battle.
If I put the PTO on the tractor in neutral (I can on my model JD 4300), the PTO turns very slowly, making alignment easy to do for that first 1/2" or so. Then punch the button and slide on the rest of the way.