Time travel wouldn’t be by jumps but by contionous change in perpendicular* time dimension.
So earth wouldn’t escape from your feet as you would move with it, just like you are doing right now with just one dimension.
*time travel would be imposible if you can move only in positive direction. Then the 2nd time dimension would need to be under some funky angle (3/4π>α>1/2π and α≠π and α≠0) i am wrong
Edit: After some thought, to truly time travel the second dimension would need to be parallel to the original one but backwards. So some people would be living in reverse time. (I have seen that concept in Sci-Fi)
Still the perpendicular time dimension is too funky of a concept to truly give it up.
Why?
No
How?
Maybe
Science doesn’t answer the Why?* questions. Philosophy does.
Are we a brain in a jar living in a simulation? Are we creation of God? There isn’t an experiment that can test those hypothesizes.
* Why? has different meanings and science does answer some of them and the one that I assume you are asking is one of them that it doesn’t.