It honestly probably started in earnest with the Sega Genesis in the early 1990s. That's when console gaming started to shift away from being more a of "family entertainment" type device and more towards something marketed primarily to male teenagers on MTV.
Contrary to popular belief too, it was the Genesis that popularized the Madden NFL, FIFA, NBA Live, NHL, etc. franchises not Sony. Mortal Kombat was probably the original "dudebros blockbuster". I think Mortal Kombat is really probably the start of "dudebros culture". That was the "Call of Duty" of its day, no question.
Then it went up a notch with the introduction of the Playstation brand and up another notch with the rise of the XBox brand which brought a lot of games that probably would've otherwise been on PC (like Halo) to the console side.
It's been developing for a while.