No you just need your residence card, fill a form, sign (no hanko required) and you can open a bank account at the Post Bank. At least that's how it went 10 years ago as a student. It's easier to open an account as a foreigner there than opening an account as a citizen in France... (no appointment bullshit, no proof of residency asked)
I became a client of Sony Bank (yes, that Sony) but they would accepted "financial resident of Japan" which means people that have either 1) a work contract or 2) lived for 6 months in Japan.
It absolutely blows my mind why Japan Post is the only one to not have those restrictions.
Getting a bank account via SMBC Olive was a painless experience for me. It can all be done an app and a phone call later confirming some details. I was not employed at the time.
