OP: take a look at the new Southwest Rapid Rewards Priority card. It won’t give you status, but you can milk some of the perks to help you get some good boarding positions until you earn status. With 4 refunded A1-15 upgrades each year, and an additional $75 of refundable SW spend, you can purchase early check in or early boarding for a few flights.
If you have status on another airline, you could also check to see if Southwest is running a status match promotion or challenge once you’re ready to start flying. That might get you status for a few months.
But there’s really no way to earn status on Southwest without paid butt-in-seat flying.