The youngest US president was JFK, inaugurated in 1960 aged 43. His youthfulness and vigour was a major reason for why he received support.
Hitler was just one year older than JFK when he became Chancellor of Germany. Was Hitler, and the Nazi movement by extent, considered to be youthful?
Can't point to any specifics but I do know the movement did gather a large amount of youths, especially in the early years when the movement was still 'new' and contrasted greatly to the political stagnation of the mainstream parties. The thrill - for lack of a better word - in being part of a movement, the street parades, the spectacle of it all provided the youth with something to do and get behind.
And while maybe not directly related to youth, supposedly he didn't marry Eva Braun earlier because he wanted to be seen as an available person (probably more in the married to the state rather than the girls goin after him)