Don't put it in the dryer. It's bad for denim. Cone - who probably make that fabric - specifically advise against it.
Most Type 3s are Sanforized; I don't know about that grey, but I doubt it's STF. I wouldn't soak it; you get the full contrast between that initial crisp look, which will be more formal, then over months it will soften. Don't know why people will want to hurry the process? And without an initial soak, the wear will be distinctly better.
Basic, Mexican-made 557. Washed once. No initial soak: