Are you turning the flywheel a bit in order to get the driveshaft and crankshaft splines engaged? Sounds like it, the L/U probably isn't up far enough for the shift shaft to be the problem.
If the driveshaft indeed is engaged into the crankshaft splines, the next thing that does come up is the shift shaft alignment. You should have had the little plastic guide piece that inserts into the end of the upper shift rod and lockout rod (in the midsection). If that isn't there, the upper shift rod will just flop around and you'll have a heck of a time aligning it. Plus the reverse lock won't work (if you have one. If you have Power Trim n' Tilt, disregard).
Sometimes the shift cable preload doesn't allow the upper shift rod to align with the shift shaft, and you have to disconnect the shift cable. Then you'd move the shifter arm until the shift shaft is engaged into the upper shift arm.
Be sure your lower unit and control box are in the same gear, or the shift shaft won't line up.
Last possibility, if the rubber exhaust tube gasket in the L/U is torn, the exhaust tube can bind on the gasket. Or if the gasket is warped on one side or the other, then the tube can't seat properly. Always a good idea to put a bit of grease on the exhaust tube or on the gasket, then they'll slip together better.
The copper water supply tube should have engaged the pump already, but if there was an issue with the rubber grommet in the pump housing, that's about the last place where you'd get a hangup. You should have a thin coating of grease on the grommet (or around the circumference of the water tube).
One or more of the above is your issue, you'll just have to figure out which one! HTH & G'luck.........ed