Besides the shar'i side of when and how Hajj becomes obligatory, I would like to add that Hajj pilgrimage is a life changing experience.
As Muslims we face the holy Ka'bah on a daily basis. We relate very much to it, and if we were to visit it we will expand in our visualising of this relationship we have with the House of Allah ta'ala.
This is why travelling to Meccah al-Mukarramah at an early age will have a great impact on our identity and mould our religious personalities.
Sadly, we see that the common trend is we postpone Hajj until we are of old age, and that Hajj is only for old people. Or that we do Hajj after we get married and have children and a stable, and so on.
But this should not be the case. If from a very young age we put aside some savings for Hajj, we would be fortunate to perform this life changing pilgrimage, and benefit from its many fruits, and then frequently repeat to go there as many times as we can.
This is why I would say that the earlier one can go to Hajj, the better.
And Allah knows best.