While I buy feed for my birds, I also grow snow peas for them, and feed them the entire plant. Most of the legumes have a decent level of protein, and many of them can be grown on a homestead.
Just be aware that soybean, which is what is used in most feeds to increase protein levels, has to be specially processed to make it digestible. So, it probably won't work to grow soybean.
My turkeys adore clover, and that is a legume, so you could look up the protein content of clover. Also table pea plants (the whole plant) and lentils.
Then you will need to also make sure they can get plenty of insects or maybe fish. Can you grow tilapia where you live? Or have a source for catfish? Warning here, I have no idea how it would affect the taste of eggs or meat if you feed a lot of fish.
Chickens will eat road kill. Maybe turkeys will, too. That's protein.
There are types of worms and bugs that you can raise at home for protein for your poultry.
The true wild turkeys who provide all their own food, range over a huge area in order to obtain all they need. They also have a high death rate. But you should be able to grow a lot of what your turkeys need, and they should stay reasonably close to wherever it is that the feed is, which should mean their feed trough at your house.
I don't think layer feed has enough protein for turkeys and it certainly does not have enough protein for poults. You'll do better to start them with a more suitable feed.
You won't be able to just turn them loose and not do any work. But you could certainly grow most of their feed for most of the year. If you are willing to do the work to feed them off of what you grow, you might be able to do it.