You can do it if you really want to dig and figure out how the ISP has things put together. First step is to try to get any IP address they use in the neighborhood. Worst case if you can get any ip in the same city. You of course need the server IP you want to determine the speed.
Now the hard part and where you will learn how the internet really works.
I would start with a site called fixedorbit.com and key in the 2 ip addresses in the tools screen under AS number. What you are trying to figure out is what ISP the server company uses and it may be multiple. You then want to be sure you know what ISP your ISP uses for its uplink providers. If it is a large one they may directly connect to the server company.
So once...