First look at the Job Boards
The general visa program for mid-career professionals in the US is the H1-B program. You can see a list of visa programs here for the USA. There are data sets open to the public on the number and categories of workers awarded H1-B visas every year.
For every H1-B visa available there are roughly 2+ applicants sponsored by companies so it is a lottery in a sense in that even if you are sponsored by a company, you don't know if you will get the job.
Once you get a visa, you can look up the regulations and laws that govern switching to a green card which is a permanent residency visa and a path to citizenship.
Japanese recruiters are going to value Japanese-language ability and nationality, familiarity with the culture, as well as experience you have with Japanese customers. You can put a search into Google with keywords and jobs will pop up.