how to find serial number without power on my apple watch

You can use the Watch App on the paired iPhone, or look in the underside or band slot of Apple Watch.

How to find the serial number or IMEI for your Apple Watch - Apple Support

1. On the bottom of the box where the Watch came with.
2. On your paired iPhone. Watch app > My Watch > General > About > Serial Number > here.

On your iPhone Watch Ap go to Settings/General/About and scroll down to Serial number. Also if you saved your packaging material it will be on that as well.