A postdoc in Japan can already apply for regular funding individually. The easiest one is called “Young Scientist B”. It can only be applied for by individuals below 39 without any other fund. The total amount of fund is below 5M Yen. The average rate to get funded is about 28%. Another one with similar amount of money is called “Challenging Exploratory Research”. It is slightly harder to get, but is not exclusive as “Young B”. One can apply for this one together with “Young Scientist A”, which provides up to 50M Yen for individuals below 39. If you are above 39, the easiest one would be “Scientific Research C”. It provides the same amount of money as “Young B” without any limit on age.
The application should be submitted through your institution around October.
The result is available around April 1st next year. It is very time consuming to fill the application form. If it is your first time, it would be too late to start in September. You would not even be able to finish the application form.
However, most of the time you will find yourself in this situation. Do not give up! Just fill all the required items with some text and submit it! The purpose is not to get funded this time, but to go through the whole process. You will get an evaluation for the failed application in next April, which tells you how good or how bad each aspect of your proposal is. Ask for it if your institution does not help you to get an English version. You will find yourself much more prepared next time. If you simply give up this time just because you do not have time to prepare a “perfect” application, most probably you will be in exactly the same situation again next time.
It is said that an English application in experimental physics submitted by a foreigner is much more difficult to get funded than a similar Japanese proposal submitted by a local researcher. This might be true. One may not submit a proposal if he is not 100% sure that it will be approved, worrying that his idea may get stolen by Japanese referees. I have talked to some experienced researchers, who have had experience as referees. Normally, they are too busy with their own projects to steal ideas from others. It is very hard to find an idea that requires not much effort to verify. Referees prefer to spend their efforts on their own ideas.