I managed to snag a First Class seat on a cross-country flight last Tuesday, and honestly, the trick was timing. I don’t have high status, so I kept checking the "Enhance Your Trip" section in the AA app. About 48 hours before take-off, a "First Class Upgrade" offer appeared for a flat cash fee. It was cheaper than buying the seat outright at booking! If you’re a status holder, you’ll get added to the complimentary list automatically, but for everyone else, these "buy-up" offers are your best bet.