Miksa was the youngest of four children born to religious Jewish parents. The Deutches lived in the town of Bistrita in Transylvania, a region of Romania that belonged to Hungary until 1918. After 1910, the family lived in nearby Viseu de Sus. In 1922 Miksa moved to Budapest, Hungary, where he and his older brother, Pal, opened a business selling matches. In 1928 Miksa married Kornelia Mahrer.

1933-39: Miksa and Kornelia had three children, whom they raised with a religious education. Miksa and his brother were the sole distributors in Hungary of Swedish-made matches, and the business prospered. In May 1939 the Hungarian government enacted a law that limited the number of Jews who could be employed in Hungarian businesses, forcing Miksa to fire some of his Jewish employees.