He was born into a wealthy family living in the Grand Duchy of Lithuania and his father Adam Baka was a treasurer of the Mscislaw Voivodeship.
Baka entered the Society of Jesus on July 16, 1723 and in 1735 he was ordained a priest, five years later becoming a monk.
Some time in late 1730s or early 1740s, Baka left Vilna for the town of Kraslaw (now Latvia, then Inflanty Voivodeship).
Later on, Baka moved to the village of Blonie (also Livonia), where he opened his own office, which he called Missio Bakana.
Baka spent final years of his life in Vilna, where he moved for unknown reasons.