How deep can we possibly dig into the Earth?It should be "How deep could we dig into the Earth?"
Presumably, they are asking "If we had better technology i.e. drills that are miles long* how deep could they go? It's a hypothetical question - about the possible depth, not the depth we/scientist have been able to reach so far i.e. can reach.
*I don't know how deep one can drill these days?