A GET request is normally synchronous, meaning that it will wait for a response.

Please explain what you mean by "keep moving REGARDLESS of what happens at the server".
In general if you make a request like you want (an asynchronous request), you need to have code to check back upon what happened to that request while your code was doing something else. That can get complicated.

There are multiple ways to create multiple instances of your program. Each instance sends a GET and waits. But there are multiple instances of this program running at once. So the server can have multiple requests that it is processing at the same time.

Please explain further what you are intending to do?
Sometimes there are API's that can do what you want.
Sometimes there are "use policies" that restrict how many "get's" are outstanding at a given time for a particular website.

Your general question is so vague that I have no solutions.