Upvoted from -1 to 0 because the question is interesting and important; the fact that the answer seems clear to some is not cause for downvoting, in my view. (This is the Discussion section; would you have downvoted this post if it had been an Open Thread comment?)

As it happens, I don't think the answer is necessarily a settled matter, any more than time travel in general (of which this can be considered a special case) is. It seems quite possible that the universe may contain much more information about its past than we can currently envision being able to extract. (One might for instance compare the old belief that determining the chemical composition of stars was hopeless due to their distance.) Yes, thermodynamics may imply that not all of the past can be reconstructed, but it may not be necessary to extract all of it in order to reconstruct a few human minds. Presumably a huge (by present standards) expenditure of negentropy would be involved, but as far as I know the universe seems to contain a whole lot of "wasted" negentropy at the moment.