I've been in a few Home Depot stores - Maine, New Hamshire, virginia, Massachusetts, Louisiana, Texas and Puerto Rico. I think that's a good enough sample for me to assure you that you didn't get Baltic Birch.Actually, I read recently Home Depot is trying to settle all kinds of problems with South American countries where they source most of their plywood. The stuff they import is really, exceptionally poor. I buy it all the time because it's convienient, but it offers nothing else. They sell something they call "sanded plywood". The face veneers look really great, A-A. When you cut it or run a router into it little islands within the wood catch fire. Little embers. Weird. Sometimes they fly out of the cut glowing like you were at a grinding wheel.
You can buy 20 X 30 pieces and larger of Finnish or Baltic birch on the internet - Do a Google search. They will want to cut it to facilitate shipping. The full panels are 60" X 60" so the cut pieces will be multiples of those dimensions.
If you want to do something economical with solid wood try poplar. Really stinks (to me at least) when you cut it but it certainly is beautiful stuff to work with. Trying finishing it with some milk paint.
White Pine and similar softwood is actually some of the hardest wood to work with. You need incredibly sharp tools to cut it cleanly, and keeping a sharp molded or square edge is nearly impossible.