I'm concerned about your fixation on one position and the thinking that clearly this low-prestige position must want you if Google is interviewing you. This could be seen as belying a deep-seeded ego/narcissism that will make you very difficult to work with. It also points to a lack of experience in the interviewing process. You really should do some self-examination before you get to the interview, because you do NOT want to convey that impression to them.
Regardless, the answer is No, it is not appropriate to call the recruiter and explain why you're the best fit. The simple reason is YOU DON'T KNOW YOU ARE THE BEST FIT. You don't know any of the circumstances of the position. Maybe the description isn't accurate. Maybe the position has been filled. Maybe there are other requirements that they're not saying openly (like they prefer an internal candidate or have someone in mind).
You could follow up to show your continued interest, but it unless you are given an interview of some form it's not appropriate to start "selling" them.
Treat a job search as any marketing campaign. Your resume/application is just an advertisement. Does Geico get upset when I turn off the TV instead of calling them to buy car insurance? No. Do they call me to try to persuade me that I should be spending my next 15 minutes to save that 15%? No. They move on to the next one and focus on building their brand in a way that maybe I'll want to buy from them in the future, or maybe my friends will. If I call them, THEN they engage in "selling" me, but until then it is basically harassment (they don't know for sure I still have a car even). They also want my experience to be excellent so I'll have a good impression of them and maybe buy additional services (i.e. get a promotion in the future). My apologies if people don't get the reference, but using a real company helps make the point clearer.
You are the product and the marketing department. Cast a wide net - you only need one buyer right now, but will likely need others in the future.