I think starting during a void moon makes it invalid and you have to wait until the next Sunday and start over again.
I started the Sun square in the first hour of the Sun for Sunday, which was at about 7:00AM where I live, and the void moon didn't happen until around 11:00AM So I think im in the clear with my Square.
I remember seeing a post saying that you shouldn't start squares during a void moon, even if the squares have nothing to do with the moon. Its a magical working the same as any other spells/meditations, so Id say that starting during a void moon will obviously make it fail the same way with any other workings.