activate phone

The phone should have powered up to the "hello" screen and walked you through the setup. Did you see a "hello" screen? If not, the phone is still locked to a previous owner and it will not be possible to setup the phone for your use.

In that case, return the phone for a refund.

If the original owner did not prepare the phone for resale, the phone will never work for you. Not even Apple will reverse the iOS activation lock.

See: The All Too Common SAD Reality of Buying … - Apple Community

If you bought a used phone, then it should have been de-registered and reset, and then it wouldn’t require connecting to a Mac or PC. Properly reset iPhones can be activated without computer.

A notification may have been send to the former user!

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

iPhone: Settings﹥General﹥Transfer or Reset [device]﹥Erase All Content and Settings.