I was thinking this is more a philosophical question and not regarding the physics.
Can a time-travel paradox prove self sustaining universe? Let's say, I create a time machine where I can send the data back in time. I create a document and send it back to myself to my past self. Now the past me doesn't need to create the document anymore because I got it from the future me.
Can this disprove the need of a creator in the universe?
If it is really true that we could go back in time and act as you stated, then i would say it suggests that there is no need for a "first step" in any chain of events. One could simply loop. In your example, no one would ever really have created the document, it would be just a loop consisting of sending it to the past, receiving it, and sending it to your past self. Your past self never created it, because you received it from your future self, and your future self never created it, because it also received it in past times.
As i understand it, that is a really complicated question. We should not say that time travel (from and to the same universe) is impossible because that would generate an inconsistent universe: It doesn't seem correct to use the consequences of an idea to disprove it. However, it does look like we live in a consistent world. My guess is that this is an argument against time travels: if, somewhere in the future, we achieved them (i mean, the ones that happen from and to the same universe), our present would not look that consistent. Conclusion: time travels must be impossible, because the universe is consistent.
