It's probably worth noting that the strongest proof of dark matter are observations of the bullet galaxy, which Vera Rubin was not involved with as far as I can tell. Some kinds of MOND (which tries to avoid the need for dark matter to explain the current state of the universe) purports to be able to explain Rubin's observations, although they cannot yet explain the bullet galaxy.
I mention this because "confirmed" is a strong word for something that we still have very little direct evidence for, other than observing the proper motion of galaxies. That's pretty strong evidence, but it'd be really cool to be able to detect the stuff directly.
Ground based experiments are testing particular models of dark matter. We know it (or some modification of gravity) exists due to its gravitational effects. Direct detection could potentially rule out the modified gravity explanation, and tell us more about what it is, but it appears disfavoured anyway (due to bullet cluster et.al.).
As others have pointed out, there are over a half dozen independent lines of evidence for something like dark matter. Prople hope more evidence such as the direct mechanical detection of WIMPS- not seen so far.
I mention this because "confirmed" is a strong word for something that we still have very little direct evidence for, other than observing the proper motion of galaxies. That's pretty strong evidence, but it'd be really cool to be able to detect the stuff directly.