Hamburg have picked up 10 points in their last four games to climb off the foot of the Bundesliga table and into the race for a place in Europe next season.
And Van der Vaart, who returned to the club from Hamburg in the summer, believes there are good times ahead.
"That is why I came back here," he told Kicker magazine. "I have the feeling that something big can happen here."
Van der Vaart does not see any reason why Hamburg cannot aim for the title in coming seasons, citing Borussia Dortmund as proof there are clubs other than Bayern Munich who can succeed in Germany.
"The club have suffered recently with 15th place last season and then the difficult start to this year, but often you have to take a step backward before moving forward again," he said.
"We are heading in the right direction and should take Dortmund as a role model."
Hamburg's recent surge in form means they are now only two points behind the defending champions and one away from a place in the top six, which would secure European football next season.