I’ll paraphrase Einstein “the distinction between the past, present, and future is a stubbornly persistent illusion”. The key to understanding that is to understand what is meant by the past, present, and future in relativity and what that really implies.
When we think of spacetime, we can think of it as being defined with 4 orthogonal axis, 3 for space and one for time. Each of these axis has tick marks either representing some unit of distance or a unit of time. We of course can’t visualize four dimensions like that, but we can picture three by suppressing one of the space dimensions. So, we can picture length and width for space (2-d plane), and use up/down for time forming a 3-d spacetime for visualization purposes. This is a reference frame by which we measure space and time.
So, how would we define the present in the above representation? Quite simply. Wherever we are on the time axis (e.g, t1) we simply define the 2-d plane orthogonal to the time axis at point t1. All points that are on that 2-d plane constitute the present. All points above that plane lie in the future, and all points below that point lie in the past.
That is fine and dandy. What happens though when we have another frame of reference in uniform motion with respect to the one we have just defined? According to relativity, the time axis of the new frame will be tilted at an angle with respect our old frame - it is no longer vertical but angled with respect to the vertical. That is the relative time axis of our new frame. Our new frames present is found in exactly the same manner - we draw a 2-d plane perpendicular to the new time axis and that constitutes the present of our new reference frame. But, now we have something very strange going on - the presents don’t match up. The planes are not parallel with each other. The new frames present can intersect with a time t2 in the future of the old frame or in the past t0 of the old frame, depending on which way the 2-d plane is tilted (which depends on whether the new frame is moving toward or away from the old frame). So, we find that the present of the two frames don’t match up, and the present of one can be the future or past of the other.
So, ready to crank up the time machine? Unfortunately, it won’t work, because causality is preserved by the equations of relativity. While the two frames don’t agree on past, present, and future, they DO agree on causal sequences. If A causes B, they will always agree on that. The fact that causality is always limited to the speed of light ensures that.