“Proxy” for streaming video

I am investigating playing live streamed video at an event venue, to a large number of Wifi connected devices. Set up would be:

Camera -> PC -> cloud streaming server (like Wowza) -> wifi AP -> devices

I'm trying to figure out how to affordably maximise the number of devices that can consume the stream in a single venue.

If the video stream bitrate is 5 Mbps then having the internet connection quickly becomes the bottleneck; with a limit of 20 users on a 100 Mbps connection.

I'm wondering if I could set-up some kind of proxy for the video stream, that would cache the stream locally to the venue and then the devices could connect to that instead.

In searching for solutions I came across a hardware proxy that could do this, but it was 10's of thousands of pounds which is not viable for my budget.

So, I'm wondering is there is a server software solution?

Secondly I've been trying to find out the limits on Wifi APs. Standard APs appear to top out at ~100 users and are then limited by their ethernet connection - say 1 Gbit.

Is it possible to set up an AP that can use a 10 Gbit ethernet and can handle order 1000 connections?

Thanks for any pointers.