That the moon reflects the sun. This does not stop the moon from being a light to us, the full moon is enough to see quite well at night. So I believe that God made the two great lights and also that it is reflecting the sun.
The first light was neither the sun, moon or stars even though there was a day and night cycle. The light seems to be something else. Perhaps it was the suns light without the sun actually being present yet. We can only guess.
3 Then God said, “Let there be light”; and there was light. 4 And God saw the light, that it was good; and God divided the light from the darkness. 5 God called the light Day, and the darkness He called Night. So the evening and the morning were the first day.
I tend to believe God didn't make them first because a lot of ancient civilizations worship them, especially the sun. Making them later lessons their importance.
6 And God said, “Let there be a vault between the waters to separate water from water.” 7 So God made the vault and separated the water under the vault from the water above it. And it was so. 8 God called the vault “sky.” And there was evening, and there was morning—the second day.
Again we have a day and night without the physical presence of the sun.
9 And God said, “Let the water under the sky be gathered to one place, and let dry ground appear.” And it was so. 10 God called the dry ground “land,” and the gathered waters he called “seas.” And God saw that it was good.
11 Then God said, “Let the land produce vegetation: seed-bearing plants and trees on the land that bear fruit with seed in it, according to their various kinds.” And it was so. 12 The land produced vegetation: plants bearing seed according to their kinds and trees bearing fruit with seed in it according to their kinds. And God saw that it was good. 13 And there was evening, and there was morning—the third day.
Third day with a day and night cycle before the 'sun' as well as growing plants. Not that plants can't survive a day and night in the dark but obviously the light was there.
14 And God said, “Let there be lights in the vault of the sky to separate the day from the night, and let them serve as signs to mark sacred times, and days and years, 15 and let them be lights in the vault of the sky to give light on the earth.” And it was so. 16 God made two great lights—the greater light to govern the day and the lesser light to govern the night. He also made the stars. 17 God set them in the vault of the sky to give light on the earth, 18 to govern the day and the night, and to separate light from darkness. And God saw that it was good. 19 And there was evening, and there was morning—the fourth day.
Since the moon is to govern the night it could not be too bright or it would turn the night into day. To me, it seems perfect just as it is.