I bought a second hand Apple Watch and it is stuck on the activation lock screen

As far as I know, the only way to remove Activation Lock is for the previous owner's Apple ID to "unpair" the watch. You can try to reach out to whoever sold it to you, but you were likely cheated.

As stated by Apple here, Activation Lock was "designed to prevent anyone else from using your Apple Watch if it's ever lost or stolen.".

Hello ~ That is the activation lock. If the person/persons that you bought the Apple Watch from cannot or will not remove it …the watch is basically useless to you. If they cannot/will not remove it…return it and get your money back. We cannot help remove it nor can Apple. Take a look here:

Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Also:

The All Too Common SAD Reality of Buying a Used iPad/iPhone

~Katana-San~