If users have the “author” role, they can upload audio and embed their music in a post. People can comment on it. This is how WP works on its own. Isn’t that the gist of Soundcloud? Of course the default audio player isn’t as nice as soundcloud’s. You could embed another player instead. There are many possibilities for other customization, either by plugin or custom code.
The basic functionality is there. What it looks like depends on the theme you select. One hurdle to overcome is audio files can be quite large. PHP default upload sizes can be a limitation. You’ll likely need a hosting plan where you can manage your own PHP php.ini settings.