Time till advanced APM
As of yet (2017) a reasonable estimation for the time-span it will take till we arrive at advanced APM systems cannot be given. Not even a crude estimation.
Methods for prediction (and their absence)
Since exploratory engineering is not applicable for answering the "when"-question one needs to turn to other less reliable methods. A popular one is extrapolating from past developments. Best example here-for is "Moores law".
But in the field of APM there's no such thing as a Moore's "law" yet (2017) that we could track. Its not even sure if such a law may even consistently occur and which metric would be used. (Throughput in units of mol/s or kg/s of atomically precise product maybe.)
The greatest question-mark on the time-spans to expect comes from the fundamental unknowability when and where we'll find the right remaining critical steps through the initial pre-percolation-limit-part of the path.
If a Moors-law-like traceable progress metric emerges (post technological percolation limit) the expectable time-spans may become at least somewhat estimable.
Scaling – What seems to be the most difficult part might actually be the easiest part
One might think that scaling up system size (and complexity) to the unconditionally required truly massive scales is the most severe hurdle. But the accelerating speed of progress in microcomputer technology suggests otherwise.
For some elaborations see: Data_decompression_chain#Bootstrapping_of_the_decompression_chain
(wiki-TODO: move this topic to Data IO bottleneck)
Possibility of exceeding Moores "law"
Especially when one considers that in contrast to Moore's law, where the production facilities (the factories) grow larger and more and more expensive, with APM not only the products regularly double in performance but also the production devices producing the products.
So once an exponential trend sets in, it cold potentially progress much more disruptively than Moore's law.
Jim Von Ehr (CEO of Zyvex) mentions this idea here .
Reactions on predictions
(Two points taken from a talk of Eric K. Drexler)
To be on the safe side we should assume that:
A) APM will come too soon for us to lean back and say:
"we don't need to think about the effects and the dangers that the arising APM technology will bring."
B) APM will come too late for us to lean back and say:
"we don't need to solve civilization problems because AP Technology will solve them."
Regarding point A:
This is one of the main reasons why we should consciously walk towards advanced APM and should not wait till we stumble in by accident. That is we should not wait till the target of advanced APM becomes painfully obvious for even the most blind.
Regarding point B:
Actually humanity does put quite some effort into research for improvement of current technology that is supposed to tackle those problems. So point B may be a bit pointless when taken as critique towards all of todays R&D. Maybe this is more meant as a precautious defense against the potentially possible criticism against APM proponents that they are neglecting point B.