Uhhh ... it's been happening for basically as long as we've known dark matter existed? The first real evidence for dark matter started coming in almost 100 years ago, in the 1930s and 1940s. The earliest dark matter models were overly simple — just treating galaxies as if they had extra mass — and they had various problems. Throughout the following decades, models of the cosmos became increasingly sophisticated ... and increasingly conflicted, as every model had some seemingly irreconcilable problems (regardless of dark matter) so it wasn't clear which model was the correct, or even the closest to correct. As I understand it, during the early 1980s the first modern models of dark matter were proposed, with distributions not matching those of baryonic matter. And with the discovery of the accelerating expansion of the universe and the need for a cosmological constant or some other form of dark energy, in the late 1980s / early 1990s, enough evidence had come in for cosmologists to hone in on a model that resolved all the issues with the previous competing models — this model is known the Lambda-CDM model (lambda is the symbol for the cosmological constant term in the Einstein field equations, and CDM stands for "cold dark matter"); it is also known as the "concordance model" because it gracefully resolved all the outstanding problems with the previous models of cosmology, and fit the data much better than any of those other models. Since that time, this model has become known as the "standard model of cosmology" and has stood out as effectively the only model that actually works and fits all of the data. Dark matter has been a part of that model since its inception in the early 90s, and in the three decades since all sorts of tweaks, additions, and parameterizations of that model (including its dark matter aspect) have been explored ... as well as many alternative models, none of which have panned out and found success at fitting all of the data well.

So dark matter has been an accepted part of the modern model of cosmology for at least 3 decades and we've had all manners of more complicated models (and attempts at alternative models) developed during that time. All sorts of supercomputing simulations of structure formation in the cosmos have been run and their statistics compared to observational datasets, with gradual refinement of the narrower strokes as new data has come in from missions like WMAP and the Planck spacecraft.

In summary, it's been happening this entire time because that's what cosmologists do — that's their job. It's not like they've been slacking off for half a century; there are tens of thousands of cosmologists and astrophysicists worldwide who have been working on it doing formal research and experimentation/observation for their entire professional careers. :)