'Starting point' tends to refer to a place rather than a time. We would understand the 'start' of the journey as when you start, and the 'starting point' as where you start out from.

I don't hear this expression often however it is used and it does make sense. :) You can also just say "It is the start of his new journey." Omitting the word 'point'. When I hear 'starting point' I think of a race or a game. You can say things like "Today marks the start/beginning of his journey." "This is where it all begins." Hope this helps!

starting point = beginning