A couple of things.

Does the trans actually fit your engine? ( designed to fit )

Was the pilot on the front of the TC and the hole in the back of the crankshaft clean ( just generally clean will do ) ? A bit of grease ( just a thin swipe ) is a good idea to prevent fretting in the long term but won't cause your install problem.

Make sure the dowel pins are in the back of the engine, sometimes these get stuck to the old trans during removal. These pins keep everything in line.

If the TC isn't fully seated in to the front pump, you will have a bind during install.

How loose are the trans to engine bolts? ( space between engine and trans )

Don't force anything, it will cause problems.