Does it matter when a time machine is invented? As soon as one has been created, couldn't you just build a second and take it back in time with you? If that doesn't work out, couldn't you just take the blueprints back with you? Wouldn't that be necessary if you wanted to get back to your original time, assuming the machine doesn't move with you?
If the machine moves with you, then there really is no such thing as "first" any more. Here's another brain teaser for you.
Hypothesis: A time machine will never be invented.
Proof: There is no one from the future among us. As soon as a time machine is invented, the chance to go back in time will exist. Since the time machine will exist off into the future from the point it is invented, the chance that someone from the future will visit our time asymptotically approaches 1. Of the set of people who would visit our time, there is a subset that would make themselves known as beings from the future and demand tribute / power / SpeedPasses at Disneyland. As time goes to infinity, the probability that such an event would occur asymptotically approaches 1.
It has not happened, therefore there will be no time machine in the future.
Image borrowed from this post over at Riff Trax. The post is worth visiting, the comment thread is pretty funny.