I was contacted months after filing out an online application. The reason for this window is that the position was posted before funding had been secured.
The process comprised of 3 interviews in this order:
1. recruiter - general questions about work history, background, and soft skills
2. technical advisor - very technical questions and most the challenging and decisive interview
3. hiring manager - confirmatory interview, general managerial skills, and to assess personality fit with the team and organizational culture
All in all a smooth, and quick process. After my first interview, I was contacted within 2 days and the second interview was scheduled within a week. And my the third interview was also scheduled within a week. Then I haven't heard form them for 2 weeks so I contacted them to inquire about the status if my application. I was told they would get back to me soon. And they did within 4 days or so with an offer.
I knew I did well in my first 2 interviews, but I wasn't sure about my third interview. The hiring manager was "multitasking" during the interview and seemed too distracted. Barely thanked me for the interview when the interview was over, and hung up so quickly I thought the internet connection was lost and without answering my questions. So when I didn't hear from them within a week as I was told by the recruiter, I thought I didn't get the job. It turns out I was their top choice and pretty much they knew they were going to make me an offer after the second interview. The delay in getting back to me after the interview process just demonstrated to me that the recruiter was exaggerating the urgency of this position. Maybe they get extra points for that, I don't know, but beware, they do that a lot.