Air carrier First Officer reported an altitude deviation due to windshear encounter on climb. Flight crew regained its cleared altitude and continued climb.

Narrative

Takeoff from ZZZ Runway XX ATC assigned hdg (Heading) 210 and 3000ft. Immediately after takeoff we began to hit moderate turbulence and on schedule PF called for The turn and Climb sequence.Shortly after at about 2400ft MSL we hit what felt like an updraft. PF began the level off at 3000ft by pitching the nose down and reducing power; but due to the updraft the aircraft continued climbing at an excessive rate and gaining airspeed. PF kept the power idle and airspeed below the Vfo speed of 230kts for about one minute before the aircraft finally began a descent again after climbing to 3600-3700ft MSL. PF leveled off at 3000ft and continued. Soon after leveling off ATC saw we were high; we reported it as wind shear.Cause: The primary cause of this event was the weather causing an unanticipated updraft. A secondary cause was the PF's failure to account for the Normal Thrust TO power and how quickly it would climb. Had the PF accounted for this and reduced power sooner during the level off then the effects of the updraft would have been less pronounced and caused less of an altitude deviation.Suggestions: Flight crews should thoroughly brief how a normal thrust TO will affect the climb out and how the weather may influence the flight path to make errors more likely.