The SWA careers page will only take so many applicants per job REQ#

Once that job REQ# hits its limit, then the request is closed and another REQ# may be created to facilitate more applications. A lot of people follow a weblink to a specific REQ# and find a dead end with a closed job listing. I can also confirm that there is no precedent on being "one of the first" or multiple job applications for the same career. In fact, it's those people who truly bog down the system and force HR to sift through redundant applications. If you got the email saying you application was received, then you are good to go.

INTERNAL RECOMMENDATIONS GO THE FURTHEST OVER HOURS/TYPES/RESUME!!!

If nobody at SWA knows you, or isn't plugging you, then don't fret waiting for an email inviting you to an interview. I interviewed in 2011 with no part 135 time and only 3700 military TT. There were plenty more qualified candidates than I was and they only had 4 classes to fill before the summer with no pilot pool to further fill. It was all about the internal recommendations that got my application moved to the consideration list.

If they say they need 200 pilots, they will likely interview 2-3 times the requirement from the total and the panel of chief pilots will be big players in determining which pilots get the nod.

Good Luck!