This question is philosophy, not science.
Define "true".
What do you mean "exist"? Does the number 1 exist? Show it to me.
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I would welcome you to attempt to define "existence" without space and time.
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You need to understand that there is a difference between the thing and the concept of the thing. try not to confuse the two.
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"You hear of physical space..." You also hear about ghosts, aliens, and esp. Your point is?
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Our best model is one in which it is wrong to separate space from time. Our Universe is a pseudo-Riemannian manifold called space-time. In it, how we separate space from time is arbitrary. It is a choice of choosing a frame of reference, a four dimensional coordinate system. Here is a metaphor (a model) for space-time. In classical physics, each instant exists next to its immediate past instant and its immediate future instant. We can look at these as if they are "stills", frames of a film. Each one in its proper sequence. When we play the movie, we see motion from past to future and all seems well. Einstein said, not quite right. Take each frame and glue it together into a solid block. Now, THAT'S the Universe. Once its glued together, we may choose to slice it up into instants any way we want.
So say event A happens in frame 101 and event B happens in frame 102. If you choose to slice it up one way then A precedes B, but if you slant your cut, you can get B into a slice that precedes A! Well, if I told you that A not only precedes B, but A "causes" B, then we have a problem. In this other frame of reference, B comes first, it can't be that A causes a past event! By making "now" relative, we have tossed a wrench into our naïve ideas about cause and effect.
There is no absolute "now". Think about the Andromeda Galaxy. "How it is now ?" has a serious logical flaw - all we can say is talk about how we perceive Andromeda "now". That is, talk about the observations of the light from it, the light that left it 2.5 million years ago.
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Most of us had geometry. We are ok with the 2 dimensional plane, and 2-D figures like lines, circles, triangles, etc. We learned the Pythagorean Theorem, and many consequences of it. Most of us were taught about how space is 3-D, and the rules are a simple extension of the rules for 2-D. So, we intuitively can grasp what 4-D space is right??
(by space, I mean space-time). WRONG! The problem is that we learned that distance between two points (in 2-D) is = √{(∆x)² + (∆y)²} and in 3-D is = √{(∆x)² + (∆y)² + (∆z)²} . And this is true for Euclidean Spaces. If it were true for space-time then the "distance" between two events would be
= √{(∆x)² + (∆y)² + (∆z)² + (∆t)²} and oh how much easier the math would be!
It turns out that the correct equation for distance in our Universe is = √{(∆t)² - (∆x)² - (∆y)² - (c∆z)² }
That "small" sign change has monumental consequences! Euclidean geometry doesn't work.
As x,y, and z increase, the "distance" between two events DECREASES. (You've probably heard that "time slows down, as you go faster" - its wrong, but there is a grain of truth in it.This negative sign is where all of the familiar paradoxes of Relativity come from. (eg the twin paradox).
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For General Relativity it is incorrect to separate time and space. I can choose coordinates so that what YOU perceive as a simple distance in space, I perceive (and can measure) as a mixture of "distance" in space and in time. Time is not useful in G.R. (But we have something we call "proper time", which takes its place there.).
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Time is useful, so I can totally change my point of view and say: anything that is as useful as the concept of time is, must exist (from this POV).
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Time means two different things. A label or a name (June 7, 2013), Guy Fawkes Day 1887... or A duration (a "distance") between two events (eg start and stop). I'll only be 10 minutes, there are 365.25 days (exactly) in a Julian year.
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The matter which comprises us and the rest of the Universe is moving through time, if you use the classical physics meaning of the word. In modern GR physics, time is an arbitrary dimension and the past and future are both as real as the present. Both are dependent on the Frame of Reference of the observer. You must be comfortable with the idea of arbitrary dimensions. In 3-D which direction is "x" ? which is "z" ? Its arbitrary, it is the set that makes the space.