FWIW, from pilot credentials
Q: Am I required to have a B737 Type Rating to be hired at Southwest Airlines?
A: A Boeing 737 Type Rating is no longer required prior to a job offer. Pilot candidates must still have a U.S. FAA unrestricted Airline Transport Pilot (ATP) certificate with an AMEL endorsement to be considered a valid applicant.
Q: I have just obtained a B737 Type Rating, how will Southwest evaluate that achievement?
A: Some candidates may have recently received a B737 Type Rating; we understand their commitment and recognize they may be targeting an opportunity at Southwest Airlines. That commitment will not go unrecognized. Even though the type rating is no longer required, it is still beneficial and will continue to have value in the screening process.