Anton Drexler was born on 13 June 1908 in Cleveland, Ohio, USA. When he was two years old, his parents returned to Slovakia, to their native village of Valča (Martin district). He was the youngest child, with two sisters and two brothers. When he was three years old, their mother died, and two years later their father died as well. Care of the children was taken over by their uncle, Anton Drexler.

He attended primary school in Valča and continued at the civic school in Martin. In 1924 he left to apprentice in artistic wood carving under Master Brieštenský in Rajec. He was a highly successful student with an exceptional artistic gift. Even as an apprentice he was a skilled carver, and Master Brieštenský frequently assigned him demanding commissions. One such example was a frame with forest motifs for a forestry engineer from Prague. When the client learned that the author was a poor boy — an orphan — he sent him money for the journey to Prague, where Drexler was offered free studies in the carving department of the State Secondary School of the Furniture Industry. He continued his studies at the School of Applied Arts, where he earned the title of academic sculptor.