How in the world do you get the sim card tray open?

It can require a significant amount of force, being careful to keep the tool straight.

Aye, both the one-year base warranty, any extended AppleCare+ coverage acquired*, plus you have 14 days to return the product no questions asked. If they can't get it open, you should get one that can.

Just be sure to back up the device and should an exchange be warranted, be sure to wipe it clean before handing it over (Settings / General / Transfer or Reset Phone / Erase All Content and Settings ).

*Now that you've experienced your first iPhone Scare might consider getting AppleCare+ if you haven't already. That will get you a new device should anything awry happen to the current one, for a service fee. Can add AC+ to an iPhone within the 60 days after getting it.

I followed the direction in this document: Remove or switch the SIM card in your iPhone - Apple Support

It can be a bit of a struggle and if need be, take it back to the Apple Store and let them do it for you.

At this point with a new phone, I would go back to the Apple Store you bought it from and ask them to open it for you. It is possible [but unlikely] that the tray is defective, only one way to know > Apple Store.

I agree with elcpu. It shouldn't be that hard. Using a lot of force may break something. The phone is new. Take it back.