Pustková made her international debut at the 2003 FIS Ladies Grand Prix , where she regularly jumped into the top 30. In 2004 she made her debut in the Ski Jumping Continental Cup and already achieved nine Continental Cup points in her first season 2004/05 and thus the 52nd place in the overall ranking. In the following season she was able to improve her performance and achieved her best result so far with 21st place in the overall ranking. At the Junior World Championships 2006 in Kranj she reached tenth place in the individual. A year later at the Junior World Championships 2007 in Tarvisio , she managed to place twelfth. In the Continental Cup, she regularly made the leap into the points and at times also made it into the top twenty, but she was still unable to build on the 2004/05 season. At the Junior World Championships 2008 in Zakopane Pustkova did not get beyond the 35th place in individual jumping. Also in 2009 in Štrbské Pleso there was no more than 28th place. At the Nordic World Ski Championships 2009 in Liberec she reached the 35th place in the individual. After the World Cup, she rarely made it into the points in the Continental Cup. At the Nordic Junior World Ski Championships 2010 in Hinterzarten , however, Pustkova again achieved a top 30 result with 26th place.