iPhone 12 Pro: Apple Watch pairing stuck on update

I am using an iPhone 12 Pro and trying to pair to a gen 1 Apple Watch that was previously paired with an iPhone that I no longer have. I factory reset the Apple Watch and my iPhone 12 Pro recognizes it and initiates the pairing process, but I am forced to download a watchOS update for version 8.8.1.

I am able to start the download, but it pauses early in the downloading process. The "Resume Downloading to Watch..." button is disabled and the error text: "You can resume the download when you are connected to a Wi-Fi network" is displayed.

Resetting either my phone or my watch forces me to restart the entire pairing process, which leads to this hard stop. Is there any way to continue the pairing process -- either with the update or without it?