Google doesn’t charge anything for SEO. First, Google doesn’t provide SEO services. All the optimization is handled without using the search engine. While you can invest in Google ads, this is not actual optimization, but sponsored content. It’s not organic or natural.
Second, Google doesn’t charge to list your website either. Websites are indexed if they meet certain criteria. The optimization will actually help your website show up higher in result pages, nothing more.
The optimization is usually performed by a professional SEO company. The actual listing and growth in ranking is something organic that Google does in a natural manner.