I think you can effectively begin sleep training at 8 weeks, but the order of E-A-S can be done from birth. There are always blips along the way for growth spurts, teeething, new skills, illnesses, and other developmental blips. But on a routine, your child will bounce back much quicker and get back on track.
Don't know what the other site is that you're talking about or their philosophy, but Tracy's philosophy is all about following the babies cues, but leading them in a direction. So, the routine is just that, a routine and not a schedule. Very few children follow exactly what the book says, but as far as generalities go, things like pt/sh instead of rocking to sleep for example, are effective and avoids the trials of breaking Accidental parenting when your child is older.
HTH