Do I need a SIM card to do it

You don't need a a SIM card to log into your Apple ID.

But you will need a working and supported SIM card if you want to make and receive calls and send and receive messages.

If the iPhone was modified by a 3rd party to remove the carrier lock and you restored it to factory settings, then it will be locked again to its original carrier. Only the carrier that it is locked to can permanently unlock it. Other unlocks will be undone when you restore the iPhone or update it to a new iOS version.

That message means your phone is carrier locked to a different network then the SIM your using. You’ll need to contact the carrier it is locked to in order to get it unlocked -> How to unlock your iPhone for use with a different carrier - Apple Support