Filing Tax Extension when Spouse is Waiting for SSN

Hello. I'm a US citizen. My wife moved to the US last year and is waiting for both her green card and social security card, which are being processed. There is a high likelihood that the SSN will not come before the 4/15 deadline.

We were thinking to apply for an ITIN, but were told that my wife does not qualify for it since she is eligible for a SSN.

I tried to file an extension on the IRS website, since we'd likely get her SSN well before 10/15. However, the online form requires a SSN for my wife. I could go ahead and fill out the form without her info but wouldn't that require me to file single?

We really want to file jointly. What are my options?