This proof assumes that time moves in one direction. But what if time isn't moving? What if we're the ones moving, at an apparently constant rate, on the X, Y, Z, and also the T axis? Imagine the universe as a sculpture, with physical size and shape, and the sculpture can be viewed from many angles. From my angle, inside the sculpture, I see things through my eyes in my location and at this time. When you read this, moments or days later, you will be seeing things through your eyes, at a different location, and at a different time. Our view of this sculpture differs because of our vantage point, just like my view of the statue of david might look like a face while yours might look like a bum.
The size and shape of the universe is enormous - billions of light years across - but it still has a size and shape. It's not like there's a beginning of width or a beginning of height. If you were to go all the way to one "end" - which is meaningless if the universe wraps around on itself, but bear with me - and then all the way to the other, you would be able to say, this universe is 16 billion light years wide. But you wouldn't call the far, far, far left side of the universe "the beginning of width". It's just the furthest left point on THIS universe. Maybe there's another universe out there, even further out. Maybe the universe will continue to grow. The X axis can go on past the end of the biggest thing there is, even if there's no real reason for it to do so.
Similarly, the universe is about 14 billion light years old. And if you were able to deliberately travel in time, you might be able to go back to a time before the universe existed, and a time after now, and look at it from the outside. On one end of the sculpture of the universe, you would see a big bang, and before that, you'd probably see nothing. Closer to here, you'd see the universe as it looks today. And if you kept moving to the far end of the universe on the other side, you'd be able to see the end of the universe, if it has one, and whatever is on the other side, if there is anything.
So if it's possible to move in time, then when you looked at the universe, you'd see its shape in space and time, and you'd theoretically be able to continue going an infinite direction to the left, up, forward, and before, because they're all just dimensions on which we'd measure your location in space/time.