Q. If one mistakenly began chazaras hashatz when there were only 9 people, realized his mistake in the middle of the 1st bracha (or any other bracha), and waited for the 10th person to return, does he now need to revert to the beginning of SE (since his earlier recital was invalid, as chazaras hashatz requires a minyan), or just continue from wherever he is now?

A. Shulchan Aruch (55: 2,3) rules that if the repetition of the amida began in the presence of a minyan and then some left, once they began with a minyan they may continue and finish this particular part of the tefila, including reciting the kadish shalem at the end. Mishna Berura (ibid.) explains, that this is true to other sections of the tefila too.
Therefore, Horav Shlomo Miller’s Shlit’a opinion is that since the repetition of the amida, which constitutes an “inyan acher” or separate part of the tefila, began without a minyan, it has to be repeated again from the beginning once the ten are present again.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a