Typically a freshman turns fifteen at some point freshman year or soon after. If a kid starts late or reclassifies once he would be sixteen.
If a kid did as you suggest he would be seventeen at some point freshman year. In most states he would be ineligible senior year in public schools for turning twenty during the academic year.
Our schools use 10/1 as the cutoff. My kid was born April 2004. He's a freshman now. He's 14. He will be 15 at the start of the season this year. But, he won't be 16 until sophomore year.
He has a classmate who was born 9/2004. He just turned 14 at the start of the school year. He won't be 15 until the start of his sophomore year. He won't be 16 until the start of his junior year.
He has another classmate who was born in July of 2003. He repeated kindergarten. He's now 15 as a freshmen. He will turn 16 just at the end of this season.
We know another kid who is a freshman. He was held back in elementary school. Then he reclassified and repealed the 8th grade. At this moment, he is 16 years and 2 months old. He also just committed to college.
We know another kid who just reclassified. He's repeating the 8th grade. He turns 15 next month. So, he will be 16 before he starts his freshman season.
In NJ, with the 10/1 cutoff, the only kids who will be playing at 16 as a freshmen are the kids who reclassified or repeated a grade.