Upload Storage?

I'm building a cloud based storage service, and my clients will be uploading quite large files.

I need these files, to first hit my server, but then move them off to an cdn. I cant! cut out my server as a "middle man" but this also means my cache will/could be clogged up before my code manage to move the files off my server and clear up space.

My question is, is there such a service, where I can run php and the disk grows as needed, up and down, so I never risk temporary running out of space, that I could use just for the upload purpose, and then my current server could handle serving static files, database calls etc.

edit I guess this is not only disk space issue, but ram issue. i have no experience with this hence why im asking, and possible for a managed solution. maybe some managed vps with such features? i dont know...

grateful for any help!