My kids have an early September and early October birthday and each of them has done some version of the whole class party early in the school year, and it’s been great.
For my DS with the early Sept birthday, when we were in a situation like this (except it was moving to a new school for pre-K), we did the small party in early august with preschool friends and I ended up regretting it. It was a lot of work and money for a party that few kids ended up being able to attend (it felt like 80% of invitees were in OBX that week) and with kids he has barely seen since then. For the next year, transitioning into K from pre-K, we did a whole class party on the second weekend of school. Literally every kid in the class came and it was a great way to meet new families.