I applied via a recruiter months before the interview. It really all depends on timing, and I was skeptical at first with a number of emails for the same position, different recruiters. A tip I used was to stick with one recruiter, hopefully with a well-known and connected agency. It doesn't matter who gets you in, but it looks bad if you have multiple sources trying to get you in.
So once I heard from the recruiter that the hiring manager wanted to interview, the interview was setup that same week. Be prepared to not only know what you're applying for, but review the company itself. Amgen prides itself on their products and culture, and wants to see how you fit in all facets of the company. The interview took place in one afternoon, with 3 in-person interviewees, and 2 on the phone. They will fire away with question after question. Be prepared to have solid questions of your own. If they're good interviewees, they'll know what is happening about the company and enjoy talking about what is up and coming. I heard back from the recruiter a few days after the interview that they wanted to hire me. As a contract position, I think they're a little more lax with the process, but it's worth it all (despite the contract length), so you can prove yourself worthy of a FTE position down the line.