Others have also
reported the 403 error when trying to listen to Beats 1 Radio. In English, the error message is: "The operation could not be completed. An unknown error occurred (403)."
It appears this message is generated when accessing Beats 1 Radio outside the United States. I also received this error, and was able to resolve it by using a VPN to connect to a VPN server in the United States.
Note: I am located in a country that is officially supported by Apple Music. AFAIK, if the country is supported by Apple Music, Beats 1 Radio should also be supported. (Apple Music appears to work fine in my country, without using a VPN connection to the United States).
I suspect this is a launch day problem that should be quickly resolved. For now, if you can, use a VPN and connect to a VPN server in the United States.