Progression of your farm in Story of Seasons: Pioneers of Olive Town is gated behind expanding your land into areas that will be locked behind different resources. In-game, you will normally need to fix something like a bridge, or clear a bunch of fallen logs, but it will always cost something.
You can choose to do it using money, or materials, and we would always suggest using materials. After you clear the bridge and expand your farm to the second area, you will need to get some solid lumber to fix up the barn you will find there. There is a cow wandering the area, and if you want to tame them, then you need the barn to put them in.
The good news is that getting solid lumber is quite easy. Make your way to the left side of the new area where the trees grow a little taller, and the leaves are a darker shade of green. Chopping down these trees is a little tougher, but doing so will get you logs that you can use to make Solid Lumber in any lumber maker.
You should already have a lumber maker from earlier in the game when you needed to fix the bridge. You will find it much easier to cut down these trees if you upgrade your axe at the tool shop to an Iron Axe.
Once you have enough Solid Lumber you can repair the barn, tame the cow, and start producing milk. Much like the chickens, you can let the cow out of the barn to eat each day so it doesn’t need too much fodder.