First Officer reported descending below approach altitude and was advised by ATC to climb and maintain minimum altitude for terrain clearance; which they did and continued the approach to landing.

Narrative

On descent into ZZZ below 10;000 feet; I recall ATC last clearing us down to 8;000 feet which is what the altitude alert was set to. I was finishing up the approach checklist as Pilot Monitoring (PM). At 8;000 feet the Check Airman in the right seat told me to push vertical speed so he could keep up with the V PATH. I asked if we were cleared for the approach and he said; 'Yes'. I believed him because of his position and how quick the situation evolved. I should have queried ATC. When we reached 7;300 feet ATC told us to maintain at least 7;800 feet for terrain. We climbed and upon reaching 7;500 feet ATC told us to cross the next fix (can't remember the name) at or above 6;200 feet; cleared approach (RNAV 16). We then recaptured the V PATH and set the altitude alert to the field elevation per FSM and landed safely. ATC didn't say anything further regarding the event. There's a chance we were indeed cleared for the approach and if so; then I missed that radio call.I should have queried ATC regarding our approach clearance. I think the procedure of keeping the altitude alert at the last cleared altitude and only letting the PM adjust it keeps both pilots in check. If the Pilot Flying (PF) wants to descend then he needs the PM to lower the altitude alert first.