Can I sync my AirPods Pro to an Apple Watch without an iPhone?

Even the cellular version of the Apple Watch requires an iPhone, as the eSIM in the Watch is a clone of your iPhone SIM, and part of the iPhone's account with your cellular carrier, it is an addition. The carrier can activate the cellular side of the Watch, and, at least here in the US, charges an additional $10/month fee on your regular cellular account. You cannot activate the cellular portion of the phone without an iPhone and account.

You would need an iPhone to pair to the Apple Watch to start out with, to activate the watch. Then you would need the iPhone to download music to the Apple Watch to be able to listen to it on the Apple Watch. Then you can pair the AirPods to the Watch to listen to music.

Now that you know you need an iPhone 6s, SE, 7 or newer, lets talk about your AirPods.

You can pair the AirPods to the Apple Watch, and listen to content stored on the Apple Watch.

When you are away from our iPhone and are using the Apple Watch as a phone, the AirPods can be used paired to the Apple Watch.

NOTE: At the moment Apple Music is the only streaming service that works on the Apple Watch.

Spotify does not provide any way to play its music on the Apple Watch.

Pandora paid subscribers and transfer offline playlists to the Apple Watch and listen to them.

You can transfer your own music, plus Podcasts and Audio books to the Apple Watch that you can listen to.

You can't use the watch at all without an iPhone, so pairing AirPods to them is a non-issue...

You're welcome.