Air carrier First Officer reported miscommunication with SCT TRACON led to descending too early during approach to MRY airport resulting in a CFTT event. ATC gave the crew a low altitude alert and instructed them to climb.

Narrative

On arrival into MRY while getting vectors to final for Runway 28L we were told to descend and maintain 6;000 feet. At about 20 nm southeast of the airport we were then told to descend and maintain 5;200 feet and report the field in sight in order to get cleared for a visual approach. However this descent put us in a position where we couldn't see the airport due to terrain in front of us. Due to the rising terrain; we approached an area where we were below the minimum vectoring altitude so air traffic control directed us to climb to 5;700 feet and subsequently gave us a low altitude alert. After passing the terrain and getting visual with the airport we were cleared for the visual approach and landed uneventfully. Upon exiting the runway and contacting ground. The Captain was told that air traffic control thought we had descended from 6;000 feet prior to receiving a clearance. Both myself and the Captain don't recall leaving 6;000 feet until we were cleared to 5;200 feet by approach. Cause - I don't remember violating any altitude restrictions given by air traffic control. I am unsure why they claim that we descended from 6;000 feet prior to receiving a clearance. The Air Traffic Controller that the Captain talked to on the phone did state that he wasn't completely sure if we had descended early since the technology that they typically use to verify our altitude record was inoperative. Suggestions - I believe that Air Traffic Control descended us to 5;200 feet too early as they anticipated that we would be able to report the field in sight and clear us for the visual approach. However; because of the terrain between us and the airport; it was impossible to see the airport resulting in ATC having to issue us a higher altitude to get above the Minimum Vectoring Altitude. In order to avoid this situation in the future; I could use better situational awareness to plan the descent; so that it is easier to see the airport and call the field in sight for a visual approach.