Sorry to nitpick a bit, dark matter isn't connected to the expansion of space (as far as we're aware) but dark energy is probably what you meant. My answer to your question is at the end.

Full disclosure: While I have studied this, my expertise was in a tangentially related field. However a buddy of mine has a PhD in measuring this stuff so I've got some second hand knowledge.

It's a confusing hurdle for any student of physics to understand that spacetime doesn't exist inside another bigger thing into which it can expand, it just kinda exists on its own. Mathematically we don't even treat the expansion quite like growth, it's a bit easier to understand it as our rulers getting shorter, the labels we give to distances changes over time. Personally I like the analogy of a sheet of grid ruled paper.

If you choose two points and count the number of squares between them, divide that grid into a smaller one and then count them again, the "distance" has gone up. Those squares look smaller to us so it seems like the true distance is the same, but the universe doesn't have an external view to make such comparisons from, all we have are the squares and physics obeys them. The point is you can cut squares up forever without running out of squares to cut up, nothing runs out this way.

In spacetime maths (general relativity aka GR) we usually start by defining distances, and when it comes to the expansion of the universe we literally just have a number in that definition that changes over time.

This kind of "our rulers and clocks are dodgy and unreliable" is unfortunately the backbone of this sort of physics. It's a huge pain in the ass, but it's cool af if you're a huge maths nerd.

How does it expand?

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Anyone who can tell you how dark energy works beyond "it has a negative pressure" is full of it. It's a theoretical idea and has never been observed, we just know that if something with negative pressure existed everywhere then it would cause space to expand. Don't quote me, but it's kinda like the opposite of how a black hole squishes spacetime down into a singularity, dark energy pushes out on everything everywhere all at once. (Couldn't help myself it's a great movie go watch it)

There are a bunch of possible things that fit the bill, it could just be a number in Einstein's field equation, it could be a specific type of quantum field that has a constant value everywhere, hell I've even seen models where it's just caused by black holes existing. It's also possible that Einstein got some stuff wrong and that expansion is just what space do. Either way, I don't think these things require more stuff to be created, it's just stuff that's already there.

If I had to make a mostly uneducated guess, I'd say it's probably just a feature of quantum gravity, for which we have no proven theories. Loop quantum gravity just demands it exists for the theory to even be useful, I'm sure string theory has it's own crazy nonsense to explain it too. If we ever do work this out, I fully expect it's just going to be a thing we have to accept exists without an obvious cause, much like how the universe exists but we have no idea why or why the rules it follows are those specific rules and not some others.