Is it possible to get an eSIM for my wireless account that uses a physical SIM?

You provided absolutely no information on what phone you have.  And my crystal ball is busted. 🔮

If your phone is capable of using an ESIM, then you probably can just have it converted. 

But without knowing what phone you have we have no idea if your phone even has an ESIM available. 🤷🏼‍♀️

I have an iPhone SE that I bought new last year. I'm sure it's capable of using eSIMs, because there is an "Add eSIM" button in the Settings. I'm not sure what the process is for having it converted. I didn't see a conversion option on the ATT website under "My Devices > Options & Settings".

The convert option for an iPhone is under settings/cellular. You should see a “Convert to ESIM” link there.

We understand wanting to convert from a physical SIM card to an eSIM solarfuel1.

To convert a physical SIM card to an eSIM, you would need to go to your local retail store location to make the switch. You can choose to make an appointment at the store location nearest you, and select a time that best fits your schedule.

Please let us know if you have any additional questions.

Thank you for reaching out to AT&T Community Forums.

Marilyn, AT&T Community Specialist

There isn't a "Convert to eSIM" button there, but maybe that's because even though the SIM card is from AT&T, at the moment I'm in Europe and maybe the local carrier doesn't support the conversion.

Yes, that’s likely the reason. I believe you need to be connected to ATT’s network and not roaming to do the conversion.

You can still convert to eSim while you are outside of the United States. You cannot activate a new AT&T SIM card outside of the United States. Choosing add ESIM is incorrect

https://support.apple.com/en-us/HT212780 

You can still convert to eSim while you are outside of the United States.

Obviously not if the convert to esim option is not there. Whether you can or not, I wouldn’t try it from outside the US.