Not to defend 12hr time because it’s dumb as a bag of bricks, but 12:45pm is definitely past noon and having the time go from 12:00am to 12:01pm would be way too silly. Also, you can think of the moment between 11:59:59.999999~ as just before noon and 12:00:00.0000000001 as the first fraction of a second after noon if it helps.