I heard nothing for four weeks after applying. The email I received was an invitation to an IQ/Personality test, which I took the same day. I sent an email after completion, heard nothing, emailed again in a couple weeks, heard nothing, and only eventually heard back when I sent a "one last try" email to follow up. An HR screening was conducted and went well. After about a week I received an invite to a conversation with the Hiring Manager, who was terrific. He said they'd be in touch with next steps, and a week later I had an invite to some team interviews in another week. Note that we're now over 2 months since I applied. These interviews were canceled a couple hours before they were scheduled to begin because they made an offer to someone else that accepted that morning. To his credit the recruiter emailed me after canceling them with the explanation.
In the end it seemed that I was always just an insurance policy in case they couldn't get the person they really wanted, who was prioritized in the process. The communications by the recruiter were mostly absent, and when present they were inconsistent. It felt quite unprofessional really. I don't hold it against the firm, it seems like some great people there and a cool industry, but this experience was a negative one. Take it as constructive criticism.