I've done it, but it was back in the days when the Japanese economy was booming. There are 3 obstacles you will face:
1) In terms of market shares and future outlook, the Japanese economic is heading towards chaos because of the longest recession it has ever experienced (+20 years). This means the Japanese economy is shrinking and not expanding. This is further worsen by their national debt which in monetary terms is half of the US national debt, but in reality is much worse because it is twice the Japanese GDP compared to the US at 108% of GDP. All this means is that international corporations do not see Japan as a good long term investment. They are in fact scaling down their presence in Japan and focusing on China. While it is possible to get an oversea assignment to Japan, you will only get there if you have key/critical expertise or experience that is needed by the branch in Japan. Do you have such expertise or experience?
2) Overseas assignment is a very much sought after position. You are not the only one who is asking for such assignments and the company will only pick from the top because you are not being sent on an all expense paid vacation and it will cost your employer more money than simply hiring someone who is already in Japan. And there are many foreigners in Japan and some of them have permanent resident status.
3) This may or may not be applicable to you, but when a company sends someone to an oversea posting, they have to consider aside from your skill sets, whether or not you are the best fit in terms of cultural assimilation. And this can take some very not so pleasant factors into account. For example your company most likely will not send a Chinese American or a Afro-American because they will not be treated less than hospitably in Japan. It's the same reason as you would not send a Palestinian to an assignment in Israel, or an Ukrainian to a posting in Russia.