The road map to space elevator (SE) development outlines what tests and demonstrations need to be done before we can build the first SE. Determination was made of activities that absolutely had to be done. They estimated the time it would take with feedback from a couple of independent people with space experience. The short summary is that there are 8 major system tests, and even with optimistic assumptions, the earliest practical date we see for commercial operation of the SE is 2031.
The announcement with links to the roadmap pdf is here