Store non-iTunes purchased music in Music on the cloud.

Hi there! I have several albums that I have purchased from non-iTunes sites (ex-7digital), and I was wondering if there was a way to store them in Music on the cloud, like how music purchased from iTunes is. I have poked around, and I do not see anything that would have iCloud sync it without me needing to store the files (FLACs that I converted to ALACs, pretty large) into a cloud storage service like iCloud files or OneDrive.

In short, like how music purchased from iTunes stays with your Music/iTunes account, I was hoping to do the same for imported files. Thanks!