I heard most of the Japanese company does not even have a tester position. Is that true?
It’s hard to speak for “most” Japanese companies, I’ve only worked directly with 3 in my life. That said, all 3 of them had at one point or another people dedicated to testing. However, I don’t think they were hired as “test engineers”, unfortunately, but were merely assigned to the role temporarily for a given project.
In general, it may be hard to get hired only as a test engineer, however having the experience and credentials alongside other skills would, I imagine, increase your value. But it just depends, you’ll have to look at jobs and see what you find.