Can nginx have client sent the request to a specific server?

If I have 3 web servers, and 1 nginx sitting in front of them (public ip
mapped to my nginx server).

My other backend servers are:

My users are upload large files, so I don’t want the request going
my nginx front-end server and then to my server.

Could it be possible to have nginx map the request to a specific backend
server and then have the request continue with that specific server?

So a request using a proxy I believe goes like this:

client request => proxy => backend-server and then it goes from
backend-server => proxy => response

But I want it to go:

client request => proxy and then backend-server => response => client

i.e. use nginx simply to map the request to a specific server, and then
client will continue the request/response with that specific server that
publicly accessible.

Now this request is a single request/response, it will not continue on.
The client is simply uploading a file or posting a file and that’s it.