Born in Dundee, Matty Smith attended Monifeith High School while playing youth football with a series of different clubs, including Fairmuir Boys, Aberdeen, Celtic and DUSC. He spent the majority of his youth career with St Johnstone, progressing through their youth ranks for seven years before he joined United in 2014 on a two year deal. He quickly became a regular with the U20/Development squad.
Towards the end of the 2015-16 season, Matty made his professional debut, selected in the starting eleven for a 3-3 draw with Patrick Thistle. On May 31, 2016, the forward signed a contract extension, keeping him at Tannadice until the summer of 2019. A loan spell at Montrose followed for the latter half of the 2016-17 season, where he played regularly for the Links Park side.