Perhaps this is off-topic or too broad to answer but I'm thinking that there must be solutions.
Some countries are talking about unplugging from the internet and creating their own isolated domestic internet. Russia, recently, ran their own tests about doing this and it has seemed successful.
How could this, essentially, large LAN network be circumvented?
It would be impossible to access resources that are not connected to the network. So, saying that direct circumvention would not be possible. Presumably, there would be limited and restricted access to external resources available to specified individuals/groups. Circumventing this restriction would be difficult, legally contentious and likely against the spirit of the question.
If we are talking about accessing external resources from a specific geographic location (which I think this question is more concerned about) than we should look at alternative methods of accessing these resources that do not require a direct physical connection.
Using satellite-based internet (such as that used on airlines) as well as connecting to adjacent regions/countries' cellular network would allow for this.
