That would rely on everybody creating timestamped proof, otherwise you could claim ownership of any paper that hasn't been timestamped by timestamping it yourself.
Not all cases are clear-cut, especially where a plagiariser restructures the document, changes the wording, sources, etc..
So I don't think this is a problem that can be solved practically, or even theoretically. But there are certainly things that can be done to better counter plagiarism.