When did mass produced FDM printers become available?
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 &quot;break-out&quot; 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.