The only thing is that you can't even create a pilot credentials profile unless you have a full ATP...it's the first question they ask.

Here's what I would do...go to create a profile, answer yes to the question asking if you have an ATP so you can create an account. However, once you are in there, there is a setting where you can choose between "draft" and "published". Get your profile all ready to go, but keep it in draft mode until the moment you get your temporary full ATP.

In mean time...get a good looking resume together. You'll need when you apply for the "window" which is separate from pilot credentials.

Do you have a college degree. If yes...great...it's a not a requirement but it's a huge part of your app score. If you don't have a college degree...can you get one? Otherwise you'll need quals like Chief Pilot, LCA, etc to overcome that.

Get some interview gouge. Think about what your TMATT questions would be.

Apply everywhere else. Competitive mins will be coming down everywhere. Being hired at another legacy and flying a 737 (or another other Boeing/Airbus) is a great way to SWA. And if SWA never works out, you'll still have a great job.