Hi -- my wife has just moved over here on an L2 visa, and is currently applying for an SSN. Do I need to wait for it to be granted before I can fill out my tax return?

Your wife can apply for an individual taxpayer identification number and use that in place of a SSN.

https://ttlc.intuit.com/replies/3300337

She has already sent off her application for a SSN. We're just waiting the two weeks for it to come through. I'm just wondering what happens if it doesn't come through before the deadline.

I was trying to find a way around it but she needs to apply for the ITIN just to use for this tax return.

Should she do this even though she has an SSN application in progress? Would the ITIN application even be quicker to come through??

It says it can take six weeks so that would not benefit you. If she does not receive her SSN by April 18 Tax Day you can apply for a time extension to complete your return.