I want to move to Japan, but I'm only 15

As stated in the title, I'm 15 and I want to move to Japan, specifically so I can work on my career as an Idol. I'm not exactly sure of the process as I am currently a homeschooler so I cannot use an exchange program. Does anybody know what the process would be? I'm proficient in Japanese, so that's not a problem, my main problem would be money.

Use your proficiency in the Japanese language to contact a few music/concert/entertainment firms and show them some of your demo videos etc. They may wish to sponsor you for a activities visa "IF" they like what they see.

In the mean time, get a job and earn money to support yourself.

At 15 and still in education there isn't much you can do right now. A foreign minor is not getting sponsored to go and live in Japan to work on becoming an idol. It simply isn't happening. There's no reason you can't get a head start though. Become a YouTuber or work on some other online platform. No, I'm being serious. You don't need to physically be in Japan (or any country) to build a brand and following there. This is 100% doable if you're good at Japanese and think you've got what it takes to actually become an idol in Japan. If in a few years time you already have a following from your food vlogs/dance cover/Vtuber videos or whatever you choose to do you are going to make an agency/producer's decision to give you a chance much more easy.

I'm not really sure if I understand your question, but if you want to know how people typically become an idol, you can Google アイドルになるには or even コロナ渦でアイドルになるには.

If you want to "work on your career as an idol", I'm sure you can practice dancing and singing at the place you currently live in.

Either way, people who are on their way to becoming a full-fledged professional idol won't have the time to properly attend schools. So, they typically enroll in a private correspondence high school, which is kind of like half-homeschooling.

And as the other poster wrote, nowadays, people make a buzz on Youtube before they are found by scouts.

As for English information on how people become idols, there is a publication written by a Harvard professor about (not J-pop but) K-pop idols, which is not too different from the way people become J-pop idols.
https://www.hbs.edu/faculty/Pages/item.aspx?num=58273

Here are other ways to be invited to Japan for your talent.
https://www3.nhk.or.jp/nhkworld/en/tv/kawaii/

Actually, your main problem would be a visa and guarantor and making sure you're taken care of by a decent agency that would sponsor them for your talent.