BTW, converting Fiat to Crypto via banks can keep you on Government radar which in-turn can be hurting to you if they want to hurt your reputation.
Not gonna happen unless you outsmart them. There are online wallets where you could cash in your fiat and use it on buying crpytocurrencies. Banks don't like transactions that is new to them, like what you have said when buying bitcoins via banks or credits cards. A lot of questions are gonna fire at you and if you don't give them the answers they wanted to hear, the worst case scenario is they will close your bank accounts and you could also lose your funds.
The last part could be a whole another story, they will accuse you that you are doing illegal things which is annoying on your part because you know you didn't do anything wrong, bank is place full of dumb ass people.