New SE Watch

It should come on when you raise your wrist if you have that configured. If you are having the tap the screen, it sounds like you have Theater Mode on. Go to the Control Center by swiping up from the bottom of the screen and check to see if the icon with the two masks it highlighted orange. If so, tap on it to turn it off. The screen should now turn on when you raise your wrist.

msbjp,

No you should not. By all means you can tap to wake the screen expecially because the Apple Watch SE does not have the always on display. You may also raise to wake by following these steps. Keep in mind, if your watch is in theater mode, raise to wake will automatically be turned off. If this did not solve your problem, please contact Apple Support or continue the thread.

1. Open the watch app on iPhone
2. Scroll down to "Display and Brightness
3. Tap "Display and Brightness
4. Click the slider to the right side of "Wake on wrist raise (Slider should become green)

Make sure this is off.