Dawid moved to live in Wrexham at the age of 15 and spent some time training at the Racecourse, whilst also playing for Airbus UK Broughton for three years.
During his time with the Wingmakers the Polish stopper spent time with Liverpool and Norwich City on trial.
In 2018 he signed for Morecambe in Sky Bet League Two joining their development side over the course of the 2018/19 campaign. Szczepaniak featured on the substitutes bench on a few occasions for the first team before departing the Globe Arena in 2019.
He joined Wrexham on trial in the summer of 2019 playing a string of games in pre-season before signing a one-year contract at the Cae Ras.
Szczepaniak made both his professional and Wrexham debut in a Tunnock's Caramel Wafer Scottish Challenge Cup tie against Ayr United at the Racecourse, saving a decisive penalty in a shoot-out following a 1-1 draw.