Have you been offered any school?
Fitting the entrance criteria fir the main admissions rounds isn't relevant.
What you need to show at appeal is that despite the school doing full, the detriment (referred to as 'prejudice') to your DS is not attending this school is greater than the detriment to the school and its existing pupils by going over numbers.
The first thing that you need to do is establish what the permitted admission number for his year group is (known as PAN) and his many pupils are currently in that year group. As they are full, the actual number will be at least PAN (because if there was a vacancy, you'd have been offered it) but you need to know if it is higher and if so by how much. It would also be useful to know what the actual numbers are in other year groups currently in the school.
What I'm getting at is if, for the sake of argument, the PAN is 150, and his year group has 152 pupils that looks a bit over-full. But if every other year group has 155 pupils, then you would have the makings of an argument that they can cope with that number and the prejudice is insignificant.
At the same time, you need to show what this schools offers that is especially important to your DS and not available (in the same way or to the same extent) in other local schools. You have the start of a case with soort. Just saying that DS plays sport (with references) and the school has a sports specialism might nit be enough. What sports does this school offer that are not available elsewere? Or does it have a coaching programme that he wouid particularly benefit from? Or fixtures?
Ditto for other interests - availability of choirs, orchestras and ensembles for the musical, regular plays and productions for thespians, particular languages not offered elsewhere, triple science etc