More specifically, we would be looking to disprove the *need* for a placeholder like Dark Matter or Dark Energy, and not the existence of any one possible candidate.
All we have now are a bunch of requirements for "something" which will make observations match existing theories/models. Some have taken that need one step further and suggested some candidates which could fulfill the requirements for the "something".
That said, no one has been able to strictly prove that the need for the required matter/energy is actually real and not some error in the model or in the observations, let alone anything which would actually fit the requirements.
However, the naming of the placeholder has given a lot of fuel to the popular notion of those concepts being a "thing" which needs to be found or disproven. Just like people believe that the "aether" is a thing that was disproven. In reality, it was the need for something like an "aether" which was ruled out. There could be something like an "aether" as conceptualized by some, but if such a thing exists, it is not the thing we needed to answer the questions we had at the time.
It is important to point this out, because ruling out dark energy or dark matter in the current context doesn't mean that something like it doesn't exist, it just means that it is no longer needed to answer these specific questions. Admittedly, if the requirements are specific enough, this is usually the same thing as the discarded notion being imaginary, but it is important to keep the context of the investigation and its conclusions in mind. We may have an instinctive idea something is correct or beautiful, and we may find it difficult to let go of that notion, so it is important to understand that discarding the use of such a concept is not ruling it out, only setting it aside because it is no longer necessary for the next steps.
I have no idea if something will be found, but until it is, we should certainly keep asking whether we have done our experiments correctly or if our understanding of the observations is accurate.
Standard candles not being standard is a fairly big deal. You need things like that to aid you in making measurements of distance for theories that span the observable universe. The Type Ia supernova standard candle has been critical for measurements at around 100 Megaparsecs and above, because they are about the only thing luminous enough to be made out at those massive distances, while still having predictable standard characteristics. This is because they can actually rival the luminosity of the entire rest of the galaxy that they are part of when they go off. Not much else can do that, and nothing else that I am aware of is expected to do it in a standard way no matter where in the universe that it happens.
There are other ways to measure distance, but the Type Ia supernovae are very widely used and studied for this reason, and so this bears some watching.
Having said all that, we didn't just measure the expanding universe based on the supernovae, the CMB and Baryon acoustic oscillations as a "standard ruler" seem to give the same data about an expanding universe. So, probably not as big a deal as has been suggested.