How to open access to a site that downloads content from other domains?

Question

Nginx

There is a local network, a gateway that looks to the Internet (linux) and an external site, such as example.com. Devices from the local network do not have access to the Internet.
It is necessary to open access from the local network only to this site, but there is a problem - the site loads data from other domains and subdomains. There are many of them, they all sit behind balancers, google APIs and other clouds in Amazon. If done through iptables, then you can drown in the abundance of accesses, proxying through Nginx is the same problem.
Advise a solution that would allow access only to this site so that it downloads the content that it needs, but no more.