I think this could be part of the solution you’re looking for: https://codex.wordpress.org/Plugin_API/Filter_Reference/wp_handle_upload_prefilter
How familiar are you with web-forms in php & file-uploads in general?
Here’s a prebuilt plugin solution for frontend uploads: https://wordpress.org/plugins/frontend-uploader/
& here’s a tutorial which looks to be along the lines of what you’re describing: https://www.inkthemes.com/code-to-integrate-wordpress-media-uploader-in-plugintheme/