C172 pilot reported an NMAC during takeoff at a non-towered airport. Pilot stopped their climb and initiated a left turn to avoid a collision.

Narrative

The incident reporter was flying a C172; on a leisure flight originating from and returning to ZZZ1.Reporter flew from ZZZ1 to ZZZ to perform practice takeoffs and landings (touch-and-go's). The flight between airports was uneventful and the entry to the traffic pattern at ZZZ was performed via the 45 entry to the left downwind for Runway XX.Traffic pattern at ZZZ was left traffic Runway XX as the prevailing winds were from the west; slightly variable but calm <5kts. Sky conditions were clear below 12000ft with greater than 10 miles visibility. There were approximately 2-3 other aircraft in the traffic pattern at ZZZ at the time of incident.At ZZZ; the reporter completed one touch-and-go without incident. During the 2nd touch-and-go; during climb in the upwind leg; the reporter received an audible ADS-B traffic proximity alert from their Garmin GDL-50 ADS-B receiver. Traffic was indicated at 2-3 o'clock; within 200' altitude; and directly converging. The reporter made visual contact with the conflicting traffic; arrested the climb; and turned slightly away from traffic - a slight (~10deg) left-hand turn from runway heading to the west/southwest. By estimation; the conflicting traffic flew 100ft overhead with minimal lateral separation. The conflicting traffic was not making radio calls; and made a nonstandard direct left crosswind entry to the ZZZ left traffic pattern at an altitude below the published traffic pattern altitude. The reporter radioed to advise the other aircraft in the pattern of the near-miss and to inform them that this aircraft had crossed the departure leg below pattern altitude without making radio calls.At the point that the reporter radioed to advise other aircraft; the conflicting aircraft started making radio calls. The other aircraft completed a full-stop landing; taxied to the apron; and shut down.The reporter completed the 2nd touch-and-go; performed a 3rd touch-and-go; and then departed to the south to return to ZZZ1.