Ignoring space for a moment, it depends whether you see time as a single - linear - dimension, or as a set of n dimensions.

If time can only exist as a single dimension, then yes, we'd have a paradox.

If time is two-(or more)-dimensional, then you'd just step into a parallel timeline/dimension for every change made, forsaking the old timeline Steins' Gate-style.

Obviously, 2+ dimensional time cannot be proven, so it's just a fun thought experiment. It's not entirely unlike the hypothetical 4th dimension of space - which would leave space-time with 4 dimensions of space and one of time.