Cessna 172 pilot reported an NMAC while in the traffic pattern. Pilot continued flight.

Narrative

On Day 0; at approximately XA:16 hours; I was PIC of Aircraft X departing ZZZ Airport. ZZZ Tower cleared Aircraft X for takeoff Runway XX. Prior to takeoff; no departure instructions were issued and I was not advised of traffic entering or established in the pattern.During initial climb; I asked Tower if a left turn out was approved. ATC then advised of traffic on left downwind and asked if I had the traffic in sight. I visually acquired the aircraft several hundred feet below my altitude passing under my left wing.The other aircraft appeared closer to the airport than a standard traffic pattern and did not appear to have entered downwind via a 45-degree entry. The pilot of the other aircraft later stated they performed an dive; however; from my perspective; the aircraft was already below my altitude and no abrupt maneuver was observed.Lessons Learned: Advising departing aircraft of pattern traffic prior to takeoff and increased awareness of non-standard pattern entries may reduce the risk of similar conflicts.