The day actual doesn’t start at midnight. Officially the astronomical day starts at noon, when the sun is highest in the sky. This is exactly at opposite side, of the earth, of Meridian 0^ in Greenwich. So it is 12 midnight in Greenwich, and exactly 12 noon on the other side of the world. Midnight is the start of our what we consider a ‘day’, and high noon is what is traditional considered the start of the astronomical day.
The first way to tell time was the sun dial, and because sunrise varies and starting a day at noon is crazy, they picked the opposite of noon even tho there was no timekeeping mechanism that would ever read midnight.
In Jewish timekeeping the day starts/ends at sunset.
Quite apart from all these people telling you that the day used to start at sunset, I am curious as to how you came to the thought in the first place, since the moon and it’s phases do not align to hours at all.
I assumed that lunar months are delimited by full moons, but I was wrong.
Huh full moons could coincide at any time of the day, and depends on where on earth you are when it happens
