Redirecting client to servers and enable direct connection

Question

I am trying to solve a problem that appear to be simple but I can't find a clean architecture.

The problem: I have a client trying to access a server in a Local network.

   |Router|------|Client
          |         |
          |------|Server

On that server I have a webapp exposed on port X. When you are behind the router (and thus the firewall) then you can easily access the webapp and use it. I would like the same to happen when outside of the local network.

Client|------|Router|-------|Server

Easy solution: The basic solution is port forwarding and to simply open port X on the router. I don't want this solution because I can't open ports (for different reason unrelated).

Better Idea I am thinking of setting up the following architecture where a new server (called B) is introduced.

Client|------|Server B|-------|Router|-------|Server A

The idea, is that Server A will maintain a connection (socket.io or websocket) with server B. This will prevent any port forwarding as Server A is making the first move. Then if the client wants to access Server A, it will access server B that will redirect it to server A.

After the first call, Ideally I would like the client to establish a direct connection with server A, without going through B.

Questions:

• Is that possible ?
• It seems that there are tools (CND, reverse proxy) but they don't exactly fit my needs, or maybe I just don't know how to use them ?
• Which tools to use on server A and B (websocket, socket.io, Nginx, Apache ...). Both servers are using linux.

Thanks !