TRACON Controller reported missing an altitude assignment on frequency resulting in a descent below the minimum vectoring altitude.

Narrative

Aircraft X checked on my frequency inbound to runway XXR. After a short time I observed them descending below 3000 feet; which is the standard altitude to feed the final. On the playback; they did check on descending to 1500 feet. I missed the incorrect altitude. They descended through the MVA; 2700 feet; and I instructed them to maintain 3000 feet. They climbed back up to 3000 feet. I did not issue a low altitude alert because they were over the ocean and there were no obstructions in the area.Suggestion: I did not catch the pilot check-in with the wrong altitude assignment. I should have listened closer and caught the mistake before the descent below the MVA.