Internet Accessible Private Cloud

I am attempting to setup a private cloud server (using a Debian VM) that is accessible to myself and a few friends over the inteet. I have a domain name, however I do not have a public IP or access to the router to create a DMZ or port forward.

I have thought of using something like Teamviewer, but only one person would be able to use it at a time and a GUI would be needed. What other methods can be used to allow us to gain access to the server? I would prefer a solution that doesn't involve using a relay server, or a free/inexpensive solution.

Thanks.