If space-time is considered as a kind of material, then what properties make sense? Properties that can be observed, measured.
In the context of General relativity, (aggregate) properties related to curvature and rippling. Like elasticity, stiffness.
In the context of quantum physics, (discrete) properties related to quanta, energy density, charge, spin, entanglement. Like gradients, flux – “jitter and jive.” So, …
• How stiff is space-time?
(quotes) … space-time is extremely stiff … even rapid motions involving large amounts of mass [e.g., mergers of two black holes] produce only tiny wiggles in space-time.
Space-time can be distorted, but it’s very hard work.
Upon combining general relativity with quantum mechanics, we calculate that space is a kind of quivering Jell-O, in constant motion.
In gravitational waves, bending of space-time in some directions causes bending in others. – Wilczek, Frank. Fundamentals – Ten Keys to Reality. (Chapters 8, 2, 1, 8)
• Well, what bends space-time?
(quote) Bending space-time requires energy, and energy causes space-time to bend. – ibid. Chapter 8.
The cosmological constant merely recognizes the possibility that space-time itself, a material that general relativity allows to bend, push, and shake, might also have inertia. – ibid. Chapter 9.
How does the interaction of quanta at a discrete level result in bending of space-time at an aggregate level? (Like pressure on a flexible membrane.)
• How can we tell if space-time is bent?
[List of experiments]
Time gradients [a better term?] [notable experiments]
Models and metaphors, levels of description
• “Times are legion” … “a different rhythm in every different place” – dynamic “spiderweb of times”
As Carlo Rovelli remarks in his book The Order of Time, “Times are legion: a different one for every point in space.” 
* Quanta Magazine > “An Ultra-Precise Clock Shows How to Link the Quantum World with Gravity” by Katie McCormick (October 25, 2021)
(quote) In a paper posted earlier this month to the scientific preprint server arxiv.org, researchers from the lab of Jun Ye, a physicist at JILA in Boulder, Colorado, measured the difference in the flow of time between the top and the bottom of a millimeter-tall cloud of [100,000 ultracold strontium] atoms.
* Science News > “An atomic clock measured how general relativity warps time across a millimeter” by Emily Conover (October 18, 2021)
Does the variation in time flux (the different rate at which time passes at locations in space-time) bend space-time, or does bending in space-time cause variation in time flux? [A better question is …]
• “The incessant flux of quantum Grid” – dynamic equilibrium
Wilczek’s characterization of space-time is predicated on a model which he calls the Grid, a multilayer structure, a dynamic medium (“aboil with virtual particles”), whose properties are quite different from the classical ether.
(quote) The entity we perceive as empty space is a multilayered, multicolored superconductor. What an amazing, astonishing, beautiful, breathtaking concept. Extraordinary, too. – Wilczek, Frank. The Lightness of Being (p. 97). Basic Books. Kindle Edition.
And his metaphor of the Grid as an exotic (cosmic) superconductor. With condensates. 
Like the gauge bosons, all these particles would be massless but for Grid superconductivity. But Grid superconductivity gives them mass [neutrinos are a special case] and also allows the heavier ones to mix with, and thereby decay into, lighter ones in complicated ways. – ibid. (p. 169)
Emergence in space-time
From the incessant flux of the Grid and the legion of times, meaningful patterns emerge. An order via confinement. A dynamic stability via chaos.
(quote) To get the most out of the big bang theory, we need to refine our assumption that the distribution of matter early on was completely uniform. Small deviations from uniformity will do, because they get amplified by gravitational instability. – Wilczek. ibid. Chapter 7.
 How might such stiffness be quantified? By sampling reality.
We can make a pretty reliable estimate of what it takes to knock loose a piece of the condensate responsible for the Grid’s (electroweak) superconductivity. The weak force is short-ranged, but not infinitely so. The W and Z bosons are heavy, but not infinitely so. The observed range of the force, and mass of the force carriers, give us good handles on the stiffness of the condensate responsible for those effects. Knowing the stiffness, we can estimate how much energy we need to concentrate in order to break off individual pieces (quanta) of the condensate … or whatever kind of new stuff … that makes the Grid a cosmic superconductor. – Wilczek, Frank. The Lightness of Being (p. 194). Basic Books. Kindle Edition.
Also, as Wilczek remarks, the Grid’s total density is likely small; otherwise, there would be no sentient beings to observe the universe. The fact that, sort of like fish, we “swim” in the Grid easily.
And, as noted in another comment, here’s a link to a paper (PDF) by Wilczek for the MIT Physics Annual 2009, “What is Space?” The paper is a useful recap of the history of space — so-called empty space, the void, the plenum, ether; and ends with a brief overview of a toy model of quantum reality.
 See Rovelli, Carlo. The Order of Time (pp. 14-18). Penguin Publishing Group. Kindle Edition.
But if different clocks mark different times, as we have seen above, what does ‘t’ indicate? When the two friends meet up again after one has lived in the mountains and the other at sea level, the watches on their wrists will show different times. Which of the two is ‘t’?
In a physics laboratory, a clock on a table and another on the ground run at different speeds. Which of the two tells the time? How do we describe the difference between them? Should we say that the clock on the ground has slowed relative to the real time recorded on the table? Or that the clock on the table runs faster than the real time measured on the ground?
The question is meaningless. … There is no “truer” time; there are two times and they change relative to each other. Neither is truer than the other.
But there are not just two times. Times are legion: a different one for every point in space. There is not one single time; there is a vast multitude of them.
Time has lost its first aspect or layer: its unity. It has a different rhythm in every different place and passes here differently from there. The things of this world interweave dances made to different rhythms.
 In particular, Chapter 8 in Wilczek’s book The Lightness of Being is all about the Grid. His Recapitulation at the end of the chapter lists key Grid properties. For example, a metric field for space-time rigidity; a universal (nonzero) density.
And the dynamics of interactions across Grid layers (quantum dimensions).
You can visualize the quantum dimensions as new layers of the Grid. When a particle hops into these layers its spin changes, and so does its mass. Its charges—electric, color, and weak—stay the same. – Wilczek, Frank. The Lightness of Being (p. 188). Basic Books. Kindle Edition.