People often confuse "proof" and "evidence" and in the legal system we often use them interchangeably when we probably shouldn't. Proof, in a scientific or mathematical sense, is something that is irrefutable and conclusively proves the point unless the assumptions it is based on are proven false. Evidence, on the other hand, is merely something that tends to make a fact at issue in the case more or less likely to be true. (Paraphrasing Federal Rule of Evidence 401, which determines relevant evidence)
Trying to create proof that would be irrefutable such as proof of original authorship is very difficult. But amassing a bunch of evidence is usually pretty easy and often what wins court cases. If you offer a hand-written and dated ledger entry that you created a work on a certain date, and you testified to its veracity in order to get it properly admitted at court, you would likely have more proof than most people for many crucial facts in court cases. Unless there is a reason to suspect the entry is fraudulent, then often the other side won't be allowed to opine that it might be fraudulent. In civil trials, the burden of proof is on the plaintiff, however the plaintiff only needs to persuade by a standard of "more likely than not" or to put it another way 51% of the evidence. If your evidence shows that you most likely created the work, simply saying the evidence might have been faked isn't usually enough to get the defendant into a winning "less likely than not" analysis of the situation.
I have seen court cases won on the file system date in a computer, which are pretty easy to tamper with, but absent a reason to suspect tampering, was treated as strong evidence of the date of a document. You can certainly improve from that low threshold of proof, so I wouldn't go overboard trying to document your discovery in a way that is foolproof.
Registration is required in order to file suit, but you don't need to do until you are aware of an infringer. There are many benefits to registering, such as a presumption of validity after 5 years, but cases have been won by people who only registered in order to file suit.