I once owned and operated a custom woodworking shop for 27 years. I've actually used very little polyurethane because of all the inherent problems and amount of time and labor involved, unless the customer insisted on that type of finish.
The first impediment is using cheap HD plywood, I'm guessing you chose Douglas fir, which is extremely difficult to achieve furniture grade results with. No matter what is used, the grain must be raised after initial sanding, otherwise the poly will accentuate the "fuzz" from sanding. Also, DF is a coarse grained wood with obvious hard and soft places within the grain itself, which requires a lot of effort to make flat. I usually coat such wood with a diluted coat of poly to act as a sanding sealer, after my initial sanding and grain raising. Once the final finish coat of poly is down, cover the project with a cardboard box, or something similar, to keep the dust in the air from ruining the finish.
I can only guess why you chose poly as the desired finish, but I've always opted for lacquer sanding sealer and bar-top clear finish. Today this is considered "old school" but it's always worked well and has won me awards for my woodworking projects. Also, a sprayed on finish will make things much simpler.