Just married on a K-1 visa, Waiting for SSN. How to file?

I married last (2022) year using a K-1 visa. I'm US citizen. My wife and his son are still in the process of Adjustment of Status and waiting for a social security number. On forms I-765 and I-485, we checked "YES" in the following question:

"Do you want the SSA to issue you a Social Security card?"

 

For 2022 taxes, do I file jointly, separately, as head of the household, etc?

What is the best route to go?

I understand that ideally I should file "Married filing jointly".

But how can I do that without SSN?

 

I have read some postings talking about the ITIN and form W-7.
However, the form W7 is pretty clear about the ineligibility:
"Don’t submit this form if you have, or are eligible to get, a U.S. social security number (SSN)."

Please refer to this topic for further details about the option to get ITIN while waiting for SSN:

https://ttlc.intuit.com/community/taxes/discussion/is-it-possible-to-file-w7-to-get-itin-nu[product ...

 

On the other hand, I read about the option to file as "Head of the household" but this is not really my situation because we are married since June 2022. I understand that I will have better deductions with "Married filing jointly".

 

So, what are my options here? Is Turbotax considering this situation?
Will the software allow me to continue without populating the SSN/ITIN?

Is requesting an extension the only way to proceed?