When I try to open a PDF File with Adobe Acrobat Pro I get an error message saying 'Adobe Acrobat could not open this file because it is either not a supported file type or because the file has been damaged (for example it was sent as part of an e-mail attachment and wasn't properly decoded'.
Are you using Acrobat on Windows or macOS?
Are you sure that the files are actually valid PDF files? When you look at the file size, does the size look plausible? Are these files stored on an online storage service like DropBox, and are you using smart synchronization that leaves the files on the server until you try to open them?
Open the file in a plain-text editor (like Notepad). What's the first line you see?
Is that the contents of the file, or an error message?
This does sound like your file is stored on a cloud storage provider (maybe not DropBox as you indicated above, but some other service). Acrobat (or most other applications) don't know about how these files are stored, it assumes that it can just use the normal filesystem operations to find, open and read a file. When a cloud storage provider is in the middle, that software needs to react to these requests and do the appropriate things to make the file available. This is not happening in this case - hence the error message. By using Notepad, and getting this error message, you've demonstrated that it's not Acrobat's (or Notepad's) fault, but something else is not workign correctly. You need to figure out where the file is stored, and what software you need to run to get access to it.
Same problem: Acrobat does not know or care about how the files are stored. OneDrive needs to make sure that the files are available when any application tries to access them. This is a OneDrive problem. If Microsoft's own Notepad application has a problem with OneDrive, then you really cannot blame Acrobat 🙂