Edges First
The first known publication of an Edges First method is from June 1979.
Roddewig, Ulrich: Solution Guide for the Hungarian Magic Cube - June 1979.
I contacted Georges Helm about the steps in this publication and Helm kindly wrote them out. Helm's notation is K for edges, E for corners, P for permute, and O for Orient, and the letters and numbers on the left and right indicate the layers.
The steps are 1. Edges of first layer, edges of second layer, edges of last layer, solve the 8 corners.
Other Edges First solutions appeared later in 1979.
EASTER Bob;Magic cube solution – October 1979 - Position then orient all edges, position then orient all corners.
Mentions of Roger Penrose and Michael Vaughan-Lee using Edges First in David Singmaster's Notes on Rubik's 'Magic Cube'.
Bob Easter used a single sequence, F R' F' R to solve the entire cube.
A relative of Ernő Rubik, Hungarian physicist Zoltán Perjés published an Edges First method.
The steps are: First layer edges, second layer edges, third layer edges, permute all corners, orient all corners.
The original publication date is unknown. The Bibliography in Notes on Rubik's 'Magic Cube' says January 1980 for the revised version. So it was likely sometime in 1979.
This method is based on an edges first method by Roger Penrose according to Notes on Rubik's 'Magic Cube'. "Zoltan Perjés has written out an algorithm, based on Penrose's, which does D edges, middle slice edges, U edges, then corners in place and then oriented."
About Zoltán Perjés.