Good news — the Google Pixel Watch LTE supports eSIM, so you can install a data plan without a physical SIM card.
Open the Watch app on your paired iPhone, go to My Watch → Cellular. If a cellular setup option appears, your watch supports eSIM.
Some carrier and region variants of this device may not support eSIM, including versions sold with a physical dual-SIM tray in certain markets. Always confirm on the device itself using the steps above.