<p>I know very little about the history of 3D printing, except that SLA came first (in the 1980's?), and FDM development was probably held back by patents.</p>

<p>By 2016, very low price kit machines were available to hobbyists, in the &lt;€300 price range, as price-reduced clones of designs which had already seen several iterations.</p>

<p>Was this the start of the break-out of cheap FDM machines (as opposed to the >€2000 semi-professional lab budget prototyping class), or were the earlier iterations of these kit machines also suitable/adopted by hobbyists?</p>

<p>I realise that early popularity would grow exponentially, but I'm thinking particularly at what point people could build a printer without needing to compile their own firmware, solder any boards, etc.</p>

By 2016, very low price kit machines were available to hobbyists [..]
Was this the start of the break-out of cheap FDM machines
No, not by any means. The
RepRap project
started in 2005, and by 2008-2010 there were several open-source printer designs out there that were somewhat workable for hobbyists. These designs were still quite expensive, you needed to source all the components yourself and do a very significant amount of troubleshooting.
However, as early as mid-2009 you could buy a
Makerbot Cupcake CNC
for \$750 as a kit (which might have involved some soldering) or \$2500 fully assembled (presumably without soldering, but it's conceivable it was plug-and-play). Makerbot went on to become quite a successful company, piggybacking off the RepRap project and could be viewed as the "break-out" you ask about.
I purchased my first printer kit (no soldering or firmware involved) for \$500 (plus around \$150 in shipping and taxes) in February 2014; cheap hobbyist machines were commonplace well before that.