I’ll leave the “is this possible” bit to the iOS experts on the forum, but I’m currently working with some big firms and they have very strict infosec requirements.
An app accessing OneDrive, DropBox, et. al. files *without using the official APIs" would be seen by these firms a big no-no.
FYI, this is less about your app being “dangerous” and more about having controls around and logging of who and what is accessing data files.
If your app is able to access files through the Files app on iOS, this access probably wouldn’t be traceable back to your app, just the device. This is terrible from a IT security audit perspective.
I’m mentioning all of this because even if there is a way to use the Files app “today”, my guess is Apple’s going to keep making it harder and harder “tomorrow” so probably better for future Chris if you bite-the-bullet and use the official APIs.