Air Carrier Pilot reported executing a go around due to encountering Wind Shear and receiving a Ground Proximity Warning. The flight diverted to a nearby airport.

Narrative

After a 1-hour maintenance delay in ZZZ; we set off for ZZZ1. The flight was uneventful until we began to descend into ZZZ1. The forecast for our original arrival had been winds 220/6; 6 SM; BKN 100; VCSH. So; while the weather wasn't spectacular; it certainly wasn't something we were concerned about when we departed. Even at the time of the delayed departure; the weather had not changed from the forecast. Prior to top of descent; all briefings were completed. Threats acknowledged (short runway; possibly wet; landing distance; night; go-around into possible weather; autobrakes max and windshear potential). As such we choose Flaps 40; autobrakes maximum; for a landing distance of about 5;000 feet. We only had 2 selections; normal or good braking at MAX AB; after that there were no options for autobrakes; something I remarked during the brief as a definite threat given the short runway. As we descended in ZZZ1 on the arrival; we began to see numerous thunderstorms and lightning; but nothing at the airport. Below 9;000 feet it was clear and we could see the airport; but to the North; South and West; thunderstorms were everywhere and the lightning was out of a movie; turning night into day. With just one aircraft in front of us; we were on vectors to the ILS XXR. Again; no weather or Thunderstorms within 10-15 miles of the airport and the weather that was there was North; South and West of the airport. We were slowed and fully configured by the FAF. The approach was stable throughout; only with some slight deviations due to winds and light turbulence. Throughout the approach I keep thinking about the go-around and possible windshear; but knowing all along; I really don't want to have to go-around into it. As the aircraft in front of us landed and cleared the runway; we were given clearance to land at 600-700 ft. Winds were reported less than 10 knots with no gust. At about 100 feet before landing; I began to feel the airplane start to encounter some gusts; nothing unstable; just making me work for it. I remember thinking to myself; this shouldn't be this hard given the reported conditions. At about 50 feet; I began to feel the airplane sink; I added power; no luck; added more; still no luck. I made the decision in my mind to go-around; and at that exact same moment the GPWS screamed; 'Windshear; Windshear; Windshear'. Without hesitation I slammed the throttles to the forward stops; rotated to approximately 15 degrees; pushed TOGA and held my breath. For a brief moment; it seemed as if nothing happened. I'm honestly not sure if we got the warning again as I became focused on flying the plane and getting away from the ground. Within about 3-4 seconds I could see our airspeed vector immediately start a positive trend and Instantaneous Vertical Speed Indicator (IVSI) was climbing at 4;000-6;000FPM. I immediately felt we were out of the event so I began calling for the go-around configuration changes and cleaned up the airplane. However; our event wasn't over; after telling the Tower of the windshear event; we now needed to navigate the numerous thunderstorms that were West of the airport. We asked for an immediate left turn to a downwind; which was granted and kept clear of the storms. Now; we had a decision to make. Make another attempt; or divert. Having the fuel; we choose to head in the direction of another approach. ATC vectored us behind Aircraft Y who was on approach. We felt that if Aircraft Y was able to land; we would at least consider an attempt. However; as we started the approach; Aircraft Y went around for windshear. At that point; I made the decision to abandon the approach and immediately head to ZZZ2. After we completed the After Take Off checklist (for the second time); declared MIN FUEL; flew some vectors; reviewed the ZZZ2 10-7 and 9 pages; approach brief/threats and deviations for weather; we landed 'uneventfully' in ZZZ2. So; commence the debrief. What went well? First; my gut told me I should fly this leg. Despite trying to get the training done; it seemed for me to be the safest option. We all have moments like these in our IOE's. Trust yourself; if you think you should fly; then fly. This is where (CRM/TEM) Planning and Decision Making; along with leadership come in. Remember; safety is our number one priority. Next; our threat forward briefing during the descent check was critical (Situational Awareness/Communication). When I briefed the windshear escape; little did I realize I'd be using it. Also; during the maneuver; I did see my First Officer (FO) ensure the speed brakes were stowed; an outstanding back up. What could have gone better? The one part of this we didn't review was how the Pilot Monitoring (PM) responds to the windshear escape. They provide key information to you when you are in the middle of a windshear event. This won't be something I'll soon forget to mention when I brief windshear. Next; the actual windshear escape/go-around. It happens so fast in actual operation; yet in the simulator we all know it's coming; as well as; what to do and what to say. Without identifying and briefing it; I would guess the PM might not be saying anything as they are reacting to the event. In our case; the FO; after being startled by the GPWS alert; was back in the loop as I called for the go-around configuration changes. Throughout the actual windshear event; I didn't hear him say anything. During our debrief; he knew what he was supposed to say; but because of the 'startle' (distraction); by the time he gathered himself; the event was over. Also; since we hadn't reviewed it in the threat forward briefing; it was understandable given his experience. However; he was right there with me on the go-around procedures and clean up. This; I believe; was because we briefed the GA procedure and he was fully aware of his responsibilities (Communication and SA). Now the divert. Simple right; just tell dispatch and ATC; plug it into the FMC RTE page; load the approach and go (Automation/Workload Management). That is of course would be simple; if you aren't coordinating with dispatch; ATC to deviate for thunderstorms; being almost on top of the airport deviating too; and while all the while watching your fuel state getting lower and declaring MIN FUEL (time compression). This is where we could have reviewed the diversion guide in the FOM; but we choose to forgo that due to time constraints and weather. Also; as diverting airports went; ZZZ2 was the only airport that was not being affected by the weather. Furthermore; we reviewed the ATIS and NOTAMs; but did not ask Dispatch for landing data. We did however; do an evaluation of our landing data per the FM; by reviewing the 10-7 page which lists no special engine out for our landing runway (Rwy XXR; 10;200ft); and we also knew we had the landing distance based on our data from ZZZ1 and the FM. Another not so well; was we forgot to re-cruise the FMC. As a result; we were unable to load the ILS approach. I'm here to say the re-cruise; 'slipped' my mind. That led us to not being able to load the FMC ILS approach due to altitude constraints. However; I did have the FO load the ILS in the FMC; which gave us a white line depiction of the approach despite being unable to execute it. Given the VFR conditions; we were able to fly a visual approach and back it up with the ILS. Next; where is the communication with the Flight Attendants? An area that was really tough. Given the time compression; after the go-around and we deviated away from the thunderstorms; I called the Flight Attendant's and told them what happened; and let them know that we were diverting to ZZZ2. I asked the Purser if she could tell the passengers; as I just didn't have time to make a PA (Workload Management). Once we landed; we still had to coordinate with operations and the passengers upon landing to determine what to do. Keeping the people informed was my biggest concern. I went into the cabin to let the passengers know I was sorry about not getting them into ZZZ1 and for having a delay in talking to them about the divert. Given the weather everyone saw out the window; no one seemed to mind and most were thankful we were just on the ground safely. The final resolution was the flight canceled in ZZZ2 due to the ZZZ1 curfew and the passengers were bused to ZZZ1. This took almost an hour after we parked.