Loosen the screws holding the hinges so the hinges are sloppy. Insert the pin into the sloppy hinges and tighten the screws.

What Hallett said, plus a partner. One person to wiggle the door/hinge into place and hold it steady, one person to actually put the pin in.

Usually a 2 person job but loosening the hinges helps it came out it will go back in Did you change something in the door frame? Why did you remove the door ?

Wha’s good for lubricating the PIN so there isn’t so much resistance pushing it in or taking it out even when the hinge is aligned? WD-40?

Clean the pin with fine steel wool (SOS steel wool pads work well) so that it is very smooth, wash thoroughly, dry, then rub lightly with 3-in1 oil. WD-40 will not last as long as regular 3-in-1 household oil.

Are these old hinges that have been painted over a few times or are they bright and shiny metal with a clear finish?

You can upload a few photos if the hinges are still giving trouble.