Captain reported descending below FAF crossing altitude before the FAF and receiving an ATC low altitude alert. Flight crew corrected and continued to landing.

Narrative

On approach into ATL I was pilot flying when during the final approach the aircraft descended approximately 200-300ft below approach minimums. On the arrival into ATL we were told to expect a visual approach to runway 10 in ATL. ATC cleared us to 3000ft and gave us a left turn heading 360 for a base leg to runway 10. On base we were still in the clouds so we asked for an approach. ATC gave us clearance for the RNAV runway 10. Due to being initially given a visual approach I had the ILS/LOC programed in as a backup and had planned to use the PAPI for vertical guidance and localizer for horizontal. Since I was flying the aircraft I asked the FO to program the RNAV. However due to the lack of time I used the localizer to give course guidance until the FMS was programed. This is where I should have gone around and asked for more time to get properly set up for the approach. I did have the RNAV approach plate up and knew we were safe to descend to 2700ft to the final approach fix so I disconnected the auto pilot and began a decent to 2700ft. After the FO got the approach loaded and we began the approach we were still outside the final approach fix when I realized we had descended below 2700ft to around 2400ft. I immediately began correcting but we were issued a low altitude alert from ATC. They noted in the transmission they saw us climbing; this was my correction. After correcting we returned to 2700ft and we flew the rest of the approach maintaining stable approach criteria from the FAF to landing. Looking back I should not have rushed this approach and should have gone around and asked for more time to get set up for a proper RNAV approach. I believe this was caused by my decision to continue an approach we needed more time to properly prepare for. Additionally having a more common approach (RNAV vs. LOC) ready as a backup could have better prepared us for a last minute switch to an IFR approach rather than a visual.