In 2004, Galambos went to the international junior world championships for the first time, where he never reached the final. Even a year later, he did not make it through the quarter-finals in all races. In 2005 he also started for the first time at the European Championships , in which he did not advance into any final. Nevertheless, he was nominated for his first World Cup in February 2005, which took place in his home country. Here, too, he only reached the semi-finals with the relay, and the two other World Cup races of the 2005/06 season in which he started ran similarly. In his third participation in a junior world championship, he made it to the quarter-finals at least in the individual race over 1500 meters.
In the 2006/07 season, Galambos did not reach the World Cup, but successfully took part in the 2007 European Short Track Championships . There he won the bronze medal over 500 meters and was eighth in the all-round overall result when Nicola Rodigari won. He was also able to win a bronze medal at the European Championships in 2008 , this time over 1000 meters, but he never made it to the World Cup. It was only in the 2008/09 season that he was allowed to start again in the highest competition series and achieved his strongest World Cup result up to this point in the 500 meters with a sixth place.