The only way to get a solid sheet of wood is to cut it from a tree like that. So if you want a piece of solid wood as big as a sheet of plywood, you first have to find a tree that's more than 4 feet across. I live in BC where we have some of the biggest trees in the world and I'll tell you that a tree four feet across, it actually has to be more to get 4 feet wide of finished lumber because of the bark and outer layers, is pretty rare even in old growth forest.
You can buy planks 2 inches thick. If they are more than 12 inches wide, they are going to start costing you a lot of money. And ordinary milled lumber, if it's called 2 by something, is actually only 1.5 inches thick. If you want it an actual 2 inches, you're going to have to have it custom milled.
You can buy laminated planks, but they don't usually come more than 2 feet wide and an inch thick at most.
I suggest going to stores that sell lumber and familiarizing yourself with it.