How to get Apple Music on iPod Touch 1G?
There is no legal way of doing that. However, there is a number of various online and downloadable converters you can use to get a usable file from the original .m4p one.

To get the file, just go to /Music/iTunes Media/Apple Music/yourSong.m4p.

Then, open a converter and just let it work its magic.

WARNING: This way is illegal, violates Apple Music's TOS and is not at all nice. Do it on your own risk.