Or just the same pad, existing for N years. When it eventually stops operating / wears out, that time is known, and a new model is installed beside it, so that travellers can simply transfer like they do with trains or lifts.Yes, I suppose this is possible. Have transporter 'pads' that can move you from one to another in both space and time. But there has to have been a 'pad' made at the other side to be able to make the journey.
It's entirely possible that in the near future with more and more powerful computers that even if we can't be transported back in 'real life' it can be done virtually. There's an episode of Black Mirror which deals with an eternal virtual existence.
But the important part (along with the original one getting invented) is that future versions will eventually be made much simpler, smaller, etc etc, and then quite cheaply massproduced. And those are the ones that’ll get taken back in time and given to anyone and everyone to use, just like Tim Berners Lee gave everyone the World Wide Web immediately.