Pilot reported pilot flying descended below charted altitude prior to visual approach clearance resulted in altitude deviation and a TCAS RA.

Narrative

We were on the LOC DME approach to Runway XX at ZZZ; in IMC; and Tower advised us to report the field in sight. As we got the field in sight; there was frequency congestion; and I waited my turn to report the field. The Pilot in Command elected to go visual as soon as we got the field in sight; descending several hundred feet below the charted minimum stepdown altitude at ZZZZZ; but before I was able to report the field in sight to the Tower. So we had yet to be cleared for a visual approach. ATC immediately advised us to climb; and at that time we reported the field in sight and were cleared for a visual approach. We later received a DESCEND RA; but after complying with the RA and visually acquiring the traffic; we landed normally.I believe that the Captain was remembering an event from a couple of days prior; where I was the Pilot Flying and was following the stepdown altitudes using VNAV. As we were flying the approach; we got a CLIMB; CLIMB NOW RA; which we complied with by climbing; and then initiating a go-around as we were then not in a position to accomplish a stabilized approach. I believe in that case; the Captain believed that we were too high on the approach before we got the RA; and now; with that experience in mind; wanted to go down as soon as we were visual; in order to flatten our descent path. And a complicating factor; of course; is ZZZ airspace; and the need for aircraft to have to land in one direction; and to have aircraft take off towards landing traffic.But in the future; as a crew; we need to do a better job of briefing approaches; and adhering to all published altitudes; speeds; and courses as we fly them.