Air carrier Captain reported the ATC assigned altitude resulted in an ATC low altitude alert and climb to a higher altitude.

Narrative

I was conducting IOE on a new hire while operating Aircraft X (ZZZZ-LGA). It was my student's 4th day so while I was doing Check Airmen duties; I wasn't verbalizing instructions in order to see where he was in his training. On descent; NY Approach cleared us from 8;000 ft. to 2;000 ft. I read back instructions and we began our descent to 2;000 ft. Around 2;500 ft; Approach gave us a low- altitude alert and instructed us to climb to 4;000 ft. Once level at 4;000 ft.; I informed ATC that we were given 2;000 ft.; I responded with 2;000 ft and no one corrected us. Approach stated that the problem was fixed and it wasn't an issue. I asked my student what he heard and he also said he heard 2;000 ft. On a side note; Approach frequency was very congested with traffic calls.Suggestions - I looked at our profile and saw 4;000 ft as the bottom of the IAF for the ILS 4. I should have verified that ATC wanted us at 2;000 ft even if it was below the altitude for the IAF on our approach. I also could have referenced the terrain page altitudes and saw that 2;000 ft would only put us 200 ft. above the highest obstacle in our range. ATC can also take time to listen to the read back of instructions assigned to aircraft.