Update: Thought I should finish the thread - I ended up going back to my carrier and after two full days of 6+ hour phone calls and one strongly worded email, the carrier finally decided to unlock my phone. I was then able to set up my phone, access settings, and (yay!) delete the bad eSim.
Should it have taken that much time to get my carrier to unlock the phone - no. However, I think the carrier was very very generous. They shouldn't have had to unlock the phone. In doing so, they risk me taking the phone and using a different cellular service. I am sticking with them as I firmly believe they didn't do anything wrong (their customer service problem solving process definitely could be improved though). I blame Apple for this issue and guys at the genius bar (when I went the 2nd time) also agreed. There should definitely be a way to access the cellular settings of the iPhone and thus be able to add/delete eSIMS before the phone is functional/activated - just like with regular SIM cards.
If you have the same issue - good luck groveling with your carrier. The only solution is to have them unlock the phone, which is against their best interests if they want to ensure your business for that time period the phone is locked. My advice - speak up, firmly state (and restate if needed) that the only solution (stated by Apple to me) is for the phone to be unlocked. If they complain, ask why you have to be the middle man between Apple and them. Apple provided the solution (unlock the phone), if they are not happy with that solution, they should be the ones groveling with Apple.
Ultimately, if multiple carriers start complaining and stating that the user needs to be able to delete/add eSIMS before the phone is activated, I am guessing Apple will implement the fix asap!