Like the "I'm my own grandpa", paradox?
There are a few periods I'd love to live in. Just they had no indoor plumbing. I never felt I belonged in this period, but I love being able to use an. Indoor toilet 🚽
I think time "travel" to the past is possible, but only as an observer, not a participant. It would be like watching a holographic movie, but with no ability to interact. The future, I'm not so sure. There's nothing a anchor onto.
And indoor plumbing? Don't sell the past so short. There's places even today that have no indoor plumbing, while the ancient Mayas of Copán had indoor running water that could be turned on or off at will, bathtub/spas, and a sewage flushing system. And if I've read my history correctly, I believe the Romans has some very good plumbing systems.