And Elohim said, “Let lights come to be in the expanse of the heavens to separate the day from the night, and let them be for signs and appointed times, and for days and years...”
(Genesis 1:14 TS2009)

The time unit “month” is conspicuously absent from Genesis 1:14. This leads me to believe that the moon is not meant to be used for determining when a month begins.