In 1500 I'd call the rise inevitable, though dominance is a rather difficult term.
By 1511, the Portuguese were taking Malacca. In other words, Europe could go over and kick Asians around without the Asians being able to do more than stop them (as did happen aplenty; Jeddah was held by the Ottomans, the Chinese took Taiwan, etc.). This just creates a horrible disparity of power. Local rulers could fight their neighbour or the Europeans; if they beat their neighbour they win, if they beat the Europeans they might be back to square 1 next year when the next European fleet comes round.
Based on the naval situation of Europe & Asia, I find the Europeans (or North Africans who are nearly the same thing) being first to round Africa in force fairly likely - given the seas, currents, etc.
So I say most likely, but not inevitable.