Air Carrier First Officer reported they descended below the minimums on a GPS Approach into deteriorating ceilings and wind shear and were issued a Low Altitude Alert by the Tower.

Narrative

During our approach into ZZZ; we where given the RNAV GPS XX; using high LPV minimums. During the brief we added in a 2 mile fix around the FAF to give us visual awareness for the 'GPS APPROACH' callout. Our initial ATIS information we received called for 10 miles of visibility; high winds and a ceiling of 6500 ft. As we descended through the STAR and vectors to the GPS approach; weather was rapidly deteriorating. On final approach we descended down to 1700 ft. and the next altitude was of 800 ft. was set. Once approaching the 2 mile point the GPS approach was called and I started a vertical descent of 700 fpm mistaking it for the 0.2NM descent. With Windshear and poor visibility; I was focused on maintain proper airspeed to ensure no over speed occurred. The Captain was making sure we had forward visibility and when he glanced back into the cockpit he noticed we were below the snowflake. At the time we were approaching 1100 ft. and ATC made an altitude alert call. I immediately disconnected the autopilot and rejoined the snowflake and continued down on a 700 fpm descent following the guidance.No contact of the runway environment was made and a go-around was initiated. On the go-around ATC noted that multiple aircraft have gone around at this point. During this time a new ATIS had come out with a visibility of 1 1/2SM. We didn't realize this until after making it on the ground. ATC was giving weather updates stating that improving visibility was from the viewpoint of the Tower but no actual visibility was stated as well as ceiling updates. We went around and made a second attempt using the GPS XX approach and made contact with the runway environment and landed. With the favorable weather conditions upon the original ATIS information; we had an expectation bias that the weather was going to be good upon landing. Poor visibility due to dropping weather conditions and high winds caused a high workload environment. We set up a 2 mile fix around the FAF; ZZZZZ; to remind us to call out 'GPS APPROACH' callout. I mistakenly mistook the 2 mile distance from the FAF for the 0.2 mile distance to initiate the descent. With both the CA (Captain) and I in a high workload situation in poor weather conditions; the callout for 'VS' was unchecked even though the confirmation of 'VS' was made. The distraction wind shear and monitoring the airspeed caused me to not fully check the distance correctly from the FAF. This brought the aircraft to descend too early and caused the low altitude callout from ATC. Another error of the cause was a lack of experience on my part; this was my second GPS approach in a real aircraft in weather conditions. A go-around should have been made instead of continuing the approach even though forward visibility was there when we received the Low Altitude Alert. Had we known the visibility an approach into ZZZ1 would have been more reasonable. Even though the checklist for the GPS approach was briefed; it probably would have been good to go over it again once closer to the airport to ensure all callouts and actions are properly made. An ILS approach would have given us more visual awareness and a reduced workload. Checking the automatic ATIS update prior to making the second attempt. Another suggestion would be to review familiarize myself with GPS approaches more so since I have only done two at this point.