Air carrier Captain reported a wind-shear encounter after takeoff. Crew performed wind-shear recovery maneuver and continued with flight normally.

Narrative

On departure from EWR runway 22Runway we experienced a reactive windshear warning that required abandoning the SID profile and climbing through the intial cleared altitude of 2500'. While no brashier warning or pilot deviation was issued; I want to document the event for the review team in case anything gets filed; and to document the event.We were not expecting windshear; and the EWR ATIS at time of departure was indicating nice weather; with a slight right crosswind; and few clouds in the area. Because of this; we were not taking windshear precautions; and departed at Flaps 5 with reduced thrust. The altimeter setting was decreasing quickly during taxi out and we had to request updated takeoff performance numbers for the new altimeter setting during taxi. I noticed in the initial climb that we were about 10-15 knots above our initial target climb speed; still within the flight manual guidance for V2+15 - V2+25 for the initial climb segment; but on the faster end. The pitch up required to maintain this speed was approximately 18º Nose Up; which is not unusal for a domestic air carrier flight to ZZZ1. I thought I had a really good rotation rate; and was slightly surprised by the initial climb speed; that should have been the first warning" that maybe we were about to experience a windshear event. As I began the left turn to the 190 heading at 500'; we felt a small jolt on the airplane followed by a "Windshear; Windshear; Windshear" reactive windshear warning. There was a decay in airspeed and momentary loss of pitch control; the yoke felt "dead". We both immediately actioned the windshear escape maneuver; "Max thrust; stow speed breaks"; and I aggressively pushed the thrust levers to the control stops to achieve max thrust; clicked the GA switches; disconnected the autothrottles; then leveled the wings and pitched for 15º before following the FD (Flight Director) command guidance. My first officer began calling out trends with airspeed and altitude. We shortly thereafter came out of the windshear; but with max thrust; I was unable to recover the speed; altitude and thrust before making it up to about 2900'. EWR Departure was advised that we were in a windshear escape; and authorized a climb to 4000'; and then gave us a right turn direct to ZZZ. We then resumed the normal climb profile. I asked for FLCH (Flight Level Change) and clean maneuvering speed; and we cleaned up the flaps and completed the after takeoff checklist. No aircraft limitations were exceeded during the windshear escape. We debriefed the event and determined that we probably experienced a wind shift around 500' that caused the increase in performance; followed by the decrease in performance that triggered the windshear warning. We had two flight deck jumpseaters; both Captains; who also jumped right into action; verifying the windshear escape and recovery was being flown properly. We worked well as a team throughout the windshear escape.As we were on the initial climb a landing aircraft reported they experienced "low level windshear" with a loss of 15 knots over the threshold but landed out of it. EWR ATC issued Low level windshear advisories after our PIREPS. Dispatch was notified of the windshear conditions we experienced on departure as well. The rest of the flight continued normally."