New Watch doesn’t turn on

I suspect your watch has a discharged battery. A device like Apple Watch always has a slight but unavoidable battery drain even if it is shut down and powered off. The On/Off button is electronic rather than a mechanical contact so this can't be prevented but I would expect the battery to last at least 3 months before needing a recharge. Apple Watch Series 7 was discontinued when Series 8 was launched around 9 months ago, so you might have received an old stock watch which had been lurking on a stockroom shelf for many months without the battery being maintained. Unfortunately when Lithium batteries drain to absolute zero charge they often can't recover and be charged again.

I suggest you put your watch on the charger and leave it for several hours. Please see Apple's support document If your Apple Watch won't charge or it won't turn on - Apple Support for notes of what you should see. If it has not recovered and shown some signs of life after a few hours (no longer than overnight) it is likely your watch can't be charged and will not recover.

If that worst case happens the only advice I can offer is to reject the watch because it is defective, and return it to the seller, get your money refunded.