That can be tricky as you would need an address and a document to prove it. I had my "alien card" when I opend mine in 2011, but I know that that card changed in 2012, so I guess they would require the new equivalent.
You might also need a "hanko" (personal stamp) to open an account, it is not the common practive to open one only with a signature. However there is place where they can do it, like Japan Post (but you need to specifically ask for it, otherwise they will ask you to provide a stamp)
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