If there is, they don't make it obvious. Whenever I've tried setting up a stock Android phone, I've looked for a way to do so without adding a Google account, but found no such option.

Perhaps it's possible to do so by pressing or holding some obscure sequence of buttons, but in that case it is reasonable to argue that a 'hidden' option isn't really an option at all. After all, you can't hide microscopic text on a paper contract and expect signees to be bound by it.

There may be stock Android phones out there that do provide a clear option to not use a Google account, but there are certainly many phones that do not.

"Add a google account, enter your email"

On the bottom of that page in grey is a skip button. You do that and you've skipped over it.

I am using a chinese noname Android phone without a Google Account. It is somewhat useable even without Internet connection and without SIM card. For example, I can use a camera, radio, music player, a dictionary or offline maps.

China gets your data now.

That's why I thought about either routing all traffic through my server or replacing proprietary ROM with open source software.

Good luck downloading apps though. I can't see how it's necessary for Google to track all your stuff, just to permit you to download an app.

You can use third party app repositories like the FOSS-only F-Droid, or even simply download apps directly from individual creators if they release the apk.

Also there are sites that allow you to download .apk file from Google Play without Google Account.