I would like to buy Apple Watch that support esim series 6, and I need to know if I buy it from the US will be activated ?

No.

Apple Watch is region specific. A US purchased Apple watch will only work with mobile carriers in the U.S, Canada, Mexico and Puerto Rico.

See here: link-> https://www.apple.com/watch/cellular/

STC is. Saudi Arabian Carrier which does not support the Apple Watch at this time anyway.

There are 2 Apple Watch cellular radios

• Canada, U.S. Mexico, Puerto Rico

• The rest of the world

Carriers will not attempt to connect to an Apple Watch that does not use the correct radio.

If you do not get your Apple Watch in your own country, you may have to return the Apple Watch to the country where purchased to get warranty service.

If you do not get your Apple Watch in your own country, there may be country specific restrictions in the installed Apple Watch software that prevent features from working when you get home.

https://www.apple.com/watchos/feature-availability

What country are you in?.