I was in the same situation as you when I was in high school. I was a U.S. born and raised teenager with practically zero Japanese language skills, but I wanted to study in Japan. Here's what I did:
1. After graduating from high school, I enrolled in a U.S. university and took Japanese language classes.
2. In the fall of my third year of university, I applied for a one-year study abroad program in Tokyo, which would start the following August.
3. In August, I moved to Tokyo and completed the one-year course.
4. I then moved back to the U.S. and finished up a few classes I had left and graduated.
5. I applied to a Japanese company for an English-teaching job, got hired, and moved back to Japan.
6. I've now lived in Japan for 16 years, working a variety of jobs.
If you speak zero Japanese, I would also recommend waiting a few years before coming to Japan to study. While it may hurt to put your dream on hold, doing so will allow you to better prepare for your time in Japan and get more out of your experience.
Your lack of Japanese skills means you'll need to find a program where instruction is in English. But while it's possible to get by in major cities like Tokyo or Osaka speaking only English, you'll get much less out of the experience. The language barrier will make it difficult to make Japanese friends, communicate with locals, and get a meaningful understanding of Japanese society and culture. That's not to say you need to be fluent before you arrive, but a year or two of serious study of the language will help you get much, much more out of your time in Japan.
In addition, waiting until a later year of university will allow you to take classes specifically related to Japan. I was a business major, and the content of the classes I took in my first two years (basic economics, fundamentals of marketing, standard accounting) isn't really any different for classes taught in the U.S. or Japan. Studying in Japan for my fourth year, however, allowed me to take specialized classes that examined Japanese businesses position and roles in both the Japanese domestic and global economies in much greater detail than I would have been able to in the U.S. The same goes for the language and culture classes I took - because they weren't introductory-level courses, the content was much more detailed, interesting, and useful.
As for some of your specific concerns:
「Maybe i havent look at enough but the unis i saw want me to take the SAT and or get recommendation letters.」
Since you didn't attend high school in Japan, odds are you're not going to be able to directly apply to a Japanese university based entirely on your local U.S. high school grades/transcripts. It's much easier to evaluate a foreign applicant based on some sort of standardized test score (like SATs), and a letter of recommendation will also help the school get a better feel for who you are on a personal level.
「Exchange Programs are expensive」
While Japan is not as expensive as some websites/guidebooks make it out to be, it is not a cheap country to live in either. If you're looking for, cheap university-level education taught in English in Japan, you might be looking for something that doesn't exist.