P&G has a stage-gate type interview process. I applied through Indeed.com. They called fairly quickly after the application was submitted. After a brief phone interview, I had a second more in-depth interview. We discussed salary, relocation, and the like toward the end of the second call. The next step was going to be some testing, but I didn't move forward in the process. I would have needed to move closer to the job location and I was not ready to do that.

Via an internship. Internships are a very common method for P&G to recruit to R&D and seems a mutually satisfactory process. The interviews for the internship was quite demanding and focussed and all applicants had to pass a basic reasoning test. Once the job offer was made there was a choice as to location and start date.