Tomas grew up in a musical family. From his childhood, as well as classical music, he was (also) interested in Bluegrass (acoustic music of the American countryside). At the age of sixteen, he began to teach at the Summer Bluegrass Workshop in Moravia, where he met leading Czech performers of this musical genre. Several recordings have emerged from their collaborations, of which the most successful gained awards in the prestigious US magazine Bluegrass Unlimited.

In 1995 he interrupted his studies at the Conservatory in Teplice and left for the USA. Here he met Matt Glaser, Head of the string department at Berklee College of Music in Boston, who invited him to his private lessons. Mach accepted the invitation. He lived in New York, made his living as a personal driver for the family of a famous physician, occasionally played concerts, for example with Italian guitarist Beppe Gambetta, and visited Matt Glaser in Boston at Berklee College of Music.

In the autumn of 1996, a tragic family event brought him back to the Czech Republic.

In 1997 he graduated from the Conservatory in Teplice in the class of prof. Doc. Vadim Skibin from Minsk.

In Freiburg, Germany, he won a competition for a scholarship to Berklee, but he has never returned to the United States. In the summer of 1997, he performed a concert tour in Estonia with legendary American banjo player Tony Trischka. In the autumn of the same year, he became a member of the Severočeská Filharmonie  (The North Czech Philharmonics) in Teplice, where he played for two years.

Furthermore, his musical activities began to become more directed towards the area of jazz. He became a member of Ondrej Havelka's Melody Makers, and orchestra focused on the authentic interpretation of swing music of the 20s and 30s. 
Mach was also teaching at the Prague Conservatory of Jaroslav Jezek.