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We know something is out there; galaxies are rotating far too quickly for our understanding of gravity to be correct. This is based on the observable matter.
For the galaxies to be rotating at the speeds we observe, we need approx 5 times the matter we see. So it is not like we have missed 10 - 20% of the matter that interacts with electromagnetic radiation, we would have had to have missed an extra 500%
As someone else pointed out, MOND is the next most promising candidate, but it has major issues even explaining what we see. Which is why it hasn't received widespread acceptance.
I don't have an answer; I have a few ideas. It maybe that something MOND adjacent is the answer; i.e. on the largest scales spacetime "relaxes" more when there is nothing pulling on it. So near galaxies and clusters spacetime is under more stress, this stress could equate to spacetime curving more on galaxy sized scales. But on the small scales we work on the extra stress will be almost invisible.
But as for us figuring out what "dark" matter is in your lifetime, unless you are already in your 80's; I think there is a very good chance. The only thing we know for sure about dark matter, is that it interacts with gravity (spacetime). We are building some pretty epic gravitational wave detectors, bringing the detection threshold lower.