ZZ
Gilles Roux and Adam Géhin discuss the EOLine idea in 2003 or earlier.
This is a message from Gilles Roux to me about the origin of the Roux method. Before creating his method, he and friend Adam had been exploring the EOLine idea. So this is the first known discussion of the idea.
Ryan Heise's EOLine, EOCross, and F2L proposal in 2003
Ryan Heise actually found the idea in a video by Adam Géhin from when Géhin and Gilles had been testing the EOLine + F2L idea. It seems that Heise noticed the use of just L, U, and R turns to solve the first two layers, may have assumed that there wasn't a method proposal behind the idea, and proposed it as a new method. Ryan Heise links to the video in this message. It is confirmed by Gilles Roux in the below screenshot that the website is that of Adam Géhin.
Ron van Bruchem posts some orient first method ideas
Ron van Bruchem credits Ryan Heise for the early EO idea used in the above EO first methods.
Zbigniew Zborowski learns of the EO first idea at the European Rubik's Games Championship 2004 (August 7-8, 2004)
Zbigniew Zborowski's story of the origin of the method
https://web.archive.org/web/20070428175325/http://www.speedcubing.com.pl/nooks_zz.htm
"The whole thing started in 2004 in Amsterdam during the 1st Official European Championships, when Ron (van Bruchem) showed Josef (Jelink) how to arrange the cube, where in the first step we orientate all (twelve) edges. I just picked up the bacon, but it was enough for me. I knew that this approach would be the future of speedcubing."
So the origin is that Zbigniew Zborowski learned of the EO first and EOLine idea at a competition from Ron van Bruchem, who learned it from Ryan Heise on the SpeedSolvingRubiksCube Yahoo group, who (unknowingly) learned it from a video by Adam Gehin, who had been discussing the idea with Gilles Roux.
WCA page for the competition
Ron van Bruchem had been experimenting with EOCross before the ZZ method was published.
This message comes over a year before Zborowski published the ZZ method. Zborowski stated that he had learned of an EO first method from Ron. So was that method EOCross > F2L?
Zbigniew Zborowski starts discussing the method on the Polish Speedcubers Forum
Polish version
English version (Google translation)
This is just one example of discussions. This website wasn't well preserved on archive.org.
Zbigniew Zborowski creates a website. Various references to December 2006 being the creation date.