Flight instructor on training flight reported NMAC with another aircraft.

Narrative

While on an instructional flight; in preparing my student to navigate from ZZZ to ZZZ1 and then return (for an upcoming student solo cross country) we had completed the arrival and full stop and reviewed getting into and out of a non-towered field. We were departing the ZZZ1 airport vicinity; turning south on to the ZZZ VOR on an approximate 178/182 heading and tuning the comm radio to the weather for ZZZ and the Garmin 430 alerted us to a traffic alert which we noted a plane traversing from east to west (we were essentially southbound over [the] Highway around the north side of the 'stripped fields practice area'). The L3 Transponder reported they were -300' and we immediately initiated a climb. We noted they did not seem to have taken evasive maneuvers; and no other traffic was apparently affected. We were not able to get a tail number; only observing that it was a white with blue trim Cessna single engine fixed gear airplane. We continued without incident to ZZZ and landed normally.Reason for report; Though I understood this to be a see and avoid class G area; and we could not get on the practice area frequency quick enough to announce our position and intentions; we heard a transmission on the Tower frequency for ZZZ as we were entering the D (delta) airspace from another plane reporting they were nearly hit in the same vicinity that we were in.[Pilot] and I were not acting reckless; careless or with disrespect to other aircraft or safety in so much as we took this as a learning point during the debrief so he could completely understand what had happened during our flight.We reviewed the option that we could have climbed to a higher altitude before turning south as an alternate option to avoid such a situation as well as monitoring traffic and understanding the see and avoid concerns of high intensity practice areas.