I see. So, you want to access the instance from a locked down network. That’s unfortunate.
With some work, you should be able to tunnel out of the proxied networked, as long as your (current proxied) network allows you to connect to a machine outside the network (most likely your home etc.) that
a) can correct to the regular internet, and hence your EC2 instance
b) you have control over to setup a SSH tunnel.
I won’t go into details of how to make that happen, as there’s tons of blogposts on the internet about this. (Search for SSH over proxy) Here’s one such link for you to follow along. https://daniel.haxx.se/docs/sshproxy.html