Serial nos on early WA12xx

I'm new to this forum. I recently got a WA1211 Formula 1 (cream color dial) on E-bay. I've been reading about serial numbers, or lack of them. I've seen mixed statements on whether or not every authentic vintage TAG/Heuer watch has a serial number etched on the case back. I've looked at a lot of photos of the early series for sale, and could not find one with a serial number. Does that men everything out there is fake? Does anyone have one with a serial number?

U think I posted to the wrong place.

I had 15 classic F1s at one point and not one of them had a serial number.

Welcome to the forum by the way, and this might be of interest to you
https://tagheuerenthusiast.blogspot.com/2020/07/history-tag-heuer-formula-1-first.html

Thanks for the quick response. I did click the link, and the info there is pretty impressive.

Thanks!