Conrad is first mentioned by contemporary records in 1239, when he was already an adult. Historian Norbert C. Tóth argued a hypothetical Baranya branch of the kindred became extinct by the First Mongol invasion of Hungary (1241–42), thus Conrad inherited their lands in Baranya County as the closest relative within the Győr clan. Initially, he belonged to the courtiers of King Béla IV; he appeared as Master of the stewards in the court of queen consort Maria Laskarina in 1253. Former historiographical works considered that his contemporary Conrad Szák held that dignity, but historian Attila Zsoldos revealed that the office-holder named Conrad owned Alásony – as Conrad Győr dit it. By 1258 (or already 1256), he was appointed as "ispán" of Borsod County, an unusual position for a landowner from Transdanubia.