According to the book, after John Galt decided to go on strike, he first went to Francisco D'Anconia and Ragnar Danneskjöld. As John Galt stated in his speech:
It was the three of us who started what I am now completing. It was the three of us who resolved to avenge this country and to release its imprisoned souls.
Very early on, they also approached William Hastings (who had been John Galt's boss at the 20th Century Motor Company) and Hugh Akston (who had taught them at the Patrick Henry University). (William Hastings joined approximately a year later).
Richard Halley appears to have been a very early Striker, having already retired many years prior to the start of the novel.
Midas Mulligan and Judge Narragansett were also early Strikers. (In fact, Midas Mulligan was the one who established Galt's Gulch).
Can a complete timeline be derived from the book?