Hi there! How as the phone activated and when? If the phone was activated recently, sometimes it does take a few hours for the SIM card to fully activate within the phone. Typically this only takes 15 minutes to an hour, but I have heard of it sometimes taking 3-5 hours.
I would also check to make sure cellular is turned on (just in case): Settings - Cellular, make sure Cellular Data is toggled to green.
Also, was this activated at an Apple Store or a store like Best Buy or Target? If it was activated in either of these places, did they provide you with your old SIM card? I have seen it where the new SIM card that comes with the phone doesn't get activated for whatever reason, and the old SIM is still active. You may want to try putting the old SIM in the new phone if you still have it.
If it was activated at your carrier, give them a call if you have access to another phone. If you don't have another phone, I would see if you go to a physical location. They may need to replace the SIM card as the one you have may be faulty. It's uncommon, but it happens.
If all else fails, contact Apple Support through an official help channel. If you can't call, they do have a chat option if you have an tablet, computer, or any other device that can access the Internet. You can initiate chat by going to getsupport.apple.com, signing in, and following the steps there.
