Your understanding of space-time is basically flawed. Space and Time are not the same. Space = Time x Speed of Light. So they're factored with the speed of light. Not literally the same.
The real reason why SPACE is curve or wrapping around a certain object is because of gravity. Gravity pulls it toward the inner core of an object. Now, when you are going to solve for the value of TIME, it is directly proportional to SPACE because the SPEED is set to be constant. Just reckon to this simple basic formula of SPEED = SPACE (distance) / TIME . Thus, SPACE(distance) = c xTIME. Now, you can view the space(distance) as curvature of an object, but how come the time coincide with it if time counts in a straight line? NO. Time is not restricted to count time in straight line ticking. THE INSTRUMENT USED TO MEASURE THE TIME IS ALSO AFFECTED BY GRAVITY. So, it is mathematically consistent to consider that time , similar to space, are in curvature axis. They call it time dilation. Any instrument use to measure the time is also affected by gravity. Now therefore, time also follows the curvature of an object. Now, you can view that the time itself is not in the straight line.It must follow the curvature of space as what that mathematics says. So,Einstein theory is true.
Example: you are holding a classical round clock on Earth. And you're observing its ticking. As you walk on Earth, let say, for 10km (just for example), you observe that clock is continue ticking uniformly. That is, each second is perfectly the same, no change of interval. But, when you go up there in space and travel for same 10km distance, you observe that the clock is ticking of not the same interval when you're on Earth. You notice it's dilation. Why? because that instrument is pulled down or resisted by gravity. That change of ticking interval gives you a hint that the distance you're traveling is not on the straight line but curve. Your 10km travelled on Earth, would not be equal to 10km travelled in space when both are stretched like strips. Because the distance you traversed in space must have a factor of the fraction of PI = 3.1416 , that is actually an arc of a circle , arc length = (angle between end points of arc/360) x 2x pi x radius of a circular object. With this formula of arc length, it is clear that the Arc#1 on Earth's surface is not really equal to Arc#2 in space; as you see in the formula, fraction of pi is a factor. Hence, distance on Earth is not equal to distance in space.
Also, we can verify that the time in space and on Earth are really not the same. Check this: Einstein noted that the speed of light is always constant. Time on space = Arc#2 / Constant speed of light , Time on Earth = Arc#1/ Constant Speed of Light. With those equations, it is clear that time on space and time on earth are not the same.
With regard to walking back in order to make you a baby again, I will tell you that you cannot apply it to matter. Time has no relation to matter. Gravity affects the matter, not the direction of time. Bear it in your mind.
Traveling in the past to see Hello to Newton or Einstein is just an illusion. Matter keeps changing and its change unless recorded could never be seen again. However, matter change can be predicted but it does not happen ahead. You cannot travel ahead to see in person what the next phase the matter will change, No. That is not the time travel would actually mean. Time travel is the concept of moving so extremely fast, or going ahead in the future never in the past. And seeing in advance what happen to matter is never possible unless those objects also move in extremely high speed and you will see it's change of state. If you scale it down, it is the same seeing it in present time. There's no difference in observation. The only difference is the scale. You scaled up your speed together with other objects, so you both see each other of your events or change in state. But, if the other object does not scale up its motion , and you move extremely fast , it is quite impossible that you can see the future of an object which does not scale up its speed. It is predicted that you can only possibly see the future but never in the past. You can only see the future of the matter provided that there are already other matter that has already moved in advance in extremely high speed.
The term "matter" here implies all things in the universe . Anything the occupies space and has mass.
So, questioning yourself why you could not be a baby again when you walk back or even you move in extremely high speed or in a speed of light, it is because you could never return back the state of matter that have already been done. Or return back the cell divisions in your body in reverse motion until it reaches its younger cells. No, it would never be possible. There's no such thing as reverse construction. What has been done is done and continue to move in forward motion. Even if you repeat the work, still its moving in forward motion. It is just like a loop or a wheel which continues rotating but time is moving forward and never backward.