I have my wife and she's not from the US. She doesn't have a SSN and can't apply for one since she's not from here. I have to file my tax return as married. What do I do?

She's not from the US but lives here. We got married on December 2022 and I can't file my taxes without claiming myself as married, and I need some identification for her. Should I put my SSN or what do I do? We can't apply for a ITIN since we are still working for her citizenship and has no documentation to submit. Please help on this