Do not reject the place! The council, having made you one offer, is not obliged to make another. So unless you can genuinely home school, or have a private place lined up, you need to avoid the risk of no place at all.
You need to go on the waiting list for any schools he could reasonably travel to, that you like better than this one.
Tell him in a totally matter of fact way - this is not the end of the world and if he does end up there he will need to make the best of it, so you need to be at least neutral even if you can't quite manage positive today.
Then start planning your appeal/s
You need the full info from each school, so you chan check which admissions priority he was placed in, and if distance from school to home looks right, or if any other part of the admin looks wrong. If an error was made, and that error cost your DS a place that he would have been offered if no mistake had been made, then you will win at appeal (and might not even go to appeal for a clear cut case)
Also, appeals can be won on 'balance of prejudice' (or the prejudice/potential harm to DS greater than the prejudice/potential harm to the school and all its other pupils if they go over numbers.
Schools cannot admit over the PAN (permitted admission number) but done regularly,cope with numbers slightly higher. You need to find out both the PAN and the actual numbers in each year group for the last few years. Admissions authorities (school itself for VA/academy, LA for others) must provide information to help parents who wish to appeal.
Keep a record of any and all conversations with LA (email the person after phone calls with your version of what was said).
Remember you are appealing for the school/s you want, not against the allocated one.
So for each preferred school in turn, what is it they have that uniquely benefits DS (don't just say it's a better school academically/pastorally, as this may alienate the panel who know all the schools well). You need specifics - do they offer everyone triple science? (DS excellent at science, does XYZ outside school this school offers triple but currently allocated does not) - what languages are available? (DS learns Spanish, needs school that offers it to,continue) - music (one has orchestras, choirs etc). Things like availability of co-curricular clubs in areas where DS has existing (evidenced!) interest/skill would count too.