How to import high bitrate MP3 files to iPhone without iTunes?

I purchase music from sites like Beatport and Amazon, high bitrate MP3 files and music that Subscription services usually do not carry. Before I would import the files to my library and then send them to my iPhone via iTunes. This is not an option in Apple Music app.

I talked to a support rep and they said I would have to purchase a subscription so I can transfer my 100+GB of music to the iCloud and then sync it with the Music app.

There has to be another way.

[Re-Titled by Moderator]