I read the the term was coined in 2010s, but that doesn't mean that was when we became aware of it.
I think the answer to this question is not straightforward. The core of the problem is based in statistical significance testing, statistical power of studies, publication pressure, and the greed for positive rather than negative results in general. Libraries have been filled on these topics and the issue is a science-wide issue, not only confined to the Social Sciences, although the problem has been identified in this area first, and seems to be the biggest here as well (probably due to the notorious variability in people's subjective responses).
The 'replication crisis' has of course slowly grown and escalated not from one day to the next. It has started to surface likely due to small meta analyses popping up here and there, up until the point larger meta reviews surfaced and the popular scientific media got hold of the idea as well.
I have been conducting a cursory literature search and one highly cited author in the area of research on reproducibility is John Ioannidis. He has published a series of studies on the (failing) replication of genetic studies. Those publications go back to a meta review published in Nature Genetics in 2001.
I bet if you dig deeper, across other disciplines, similar articles with similar alarming messages will readily surface with publication dates long before the earliest paper from 2001 I was able to find in my search.