When you're
born. That is your
birth day, because the person to whom you were
born gave
birth to you that day.
No culture I know of tracks the date of your conception as a measure of your age. If they measure it at all, the starting point is your birth.
You are zero days old on the day of your birth. Even if those cultures think you are "in the first year of your birth" for days 0-365 of your existence, they would accept that 1 day after your birth, you are 1 day old, not 9 months old.