We have created a framework for time based on the solar system we live in, the Earth's rotation and relationship to the Sun, and that is how most of us view time. We organize our lives within that framework and mark the passing of time (birthdays, anniversaries) according to it. Aside from that, we all live as long as we are going to, some more, some less than others, some work harder or longer hours and some never work at all. So is time really all that relevant outside our desire to organize our lives and record events?
Is time travel possible? Certainly, it's possible, although it might only be so outside humans ability to understand it, or in dimensions we are incapable of perceiving. I would have to know everything about the universe to say it was impossible.