Noooo. I was a desktop software developer in the 90s and the conversation definitely started then. Remember we are talking about desktop software not web development (and by the late 90s bevels were seen as archaic as “under maintenance” GIFs).
To illustrate the timeline: Windows MSIs were often compared to Install Shield with regards to the difference between the newer flat design elements of Microsoft vs the older 3D objects of the previous iterations of Windows. By Windows 2000 Microsoft had already cemented that flat design was their way forward. Sure buttons were still 3D but a lot of other design elements had been flattened or removed entirely (panels, toolbars, image boarders, editable text areas in some cases too).
While you are right that Metro / Modern was another massive leap forward in terms of flat design, by that point Apple had already dropped much of their skeuomorphic design elements. So the discussions by that point were less about skeuomorphism vs flat design and more about accessibility concerns with regards to removing all hints of 3D in flat design. Basically by 2010 flat design had already largely won over skeuomorphic design. So while designers were still endlessly debating these things, it certainly wasn’t the start of the conversation.