Yes, it is from a tree, a apple tree. The tree is found in some places on the map although i've never found on on the island you spawn on, the first time I found the apple tree was somewhere on the left of where you spawn.Once you find one, do whatever you would do with a normal tree,chop it down. I liked using the apple tree for farming because of its slightly better drops : a log and a apple at the same time so I recommend using the apple tree for farming straight away.(but don't waste time at the starting point of a new game)
I strongly recommend using a mallet with an apple tree though, since it drops apples and you don't need to wait for the tree to regrow to harvest more apples. It also separates the log harvesting from apple harvests.
I've tried the strictly apple tree farming like you suggest, but I soon ended up with more apples than I could use and needed to make an incinerator to keep the supply from making mountains of apples. They don't despawn (like tree seeds/acorns do) and have other problems even if you are making apple pies... where the largest hold up to making more pies is actually getting enough milk from cows.
It also creates other imbalances if you don't need logs but need apples. I've also had the apple pie production halt due to a lack of apples when my log storage containers were full and comparatively few logs were being used. A real late game issue to be sure, but something to think about.
The mallet solves those issues as it gives you a reliable source of apples that you can start and stop at any time. What I do instead is simply get a few apple trees in a smaller patch of tree soil and have one worker bot per tree pounding at that tree with the mallet for apple production.