Highly skilled in the fundamentals of baseball, Welsh was a four-year varsity starter at Northern Burlington County Regional High School. He was an all-conference selection as a junior and a sophomore, and was named NJ.com Group 3 All-State in 2016, in addition to all-area and all-county accolades. He hit .405 with 24 RBIs, 12 doubles, three triples and five home runs as a senior. He also earned team defensive player of the year award in 2015. His team won the New Jersey Group III Division in his last three years and sectional champions as a freshman and a junior. Welsh played travel baseball with the Tri State Arsenal for eight years. His Arsenal 16U team was Super 25 Northeast Regional Champs, Super 25 National Champs and WWBA National Champs, all by Perfect Game. Welsh plays his college ball at Rutgers University, where he put up a stellar 2017 freshman campaign. He posted a .359 on-base percentage, a .346 batting average with runners in scoring position, a 13.5% walk rate and an excellent 9.6% strikeout rate, and 10 sacrifice bunts while starting 48 games at shortstop and 5 at second base. In 2018 Welsh picked up switch hitting for the Scarlet Knights, finishing with a .243 average, 4 doubles, 2 triples, and 21 RBI.