No ads or subscriptions, no endless DLC.
Unfortunately, if you’re looking for a free download, the game you’re describing doesn’t exist.
The closest I can think of is Postknight 2. There’s unobtrusive (optional) ads, and the full game is playable—start to finish—without spending any money.
It’s very cute, and you can get pets… but it’ll take some dedicated playtime to unlock them for free.
“What did you do this weekend?”
“I went to the second, secret Burning Man where they immolate an actual man.”