TurboTax does not use 8879 or provide a filing letter. Form 8879 if used by paid preparers. You are doing your own taxes with TurboTax and do not use 8879.
Let the financial institution know that you cannot provide those proofs of filing. Explain that you filed yourself with TurboTax and do not have them. Ask for some alternate form of proof of filing. There is an e-file number generated when you file and the helpdesk may be able to provide that number to you.
I am not sure if that is information that they can share with the taxpayer. I would suggest you call the helpdesk and ask if there is any proof of filing that they can provide to you.
In the PDF of your TurboTax return, the last page of the federal return should be an "electronic postmark" that shows your name, Social Security number, the date and time that you e-filed the return, and the date that the IRS accepted it.
Save the PDF
Form 8879 is ONLY used by paid professionals. It is to authorize the paid tax preparer to file for you. Do-it-yourself software you file the tax return so that form does not exist.
If the IRS has processed your return then they should have a transcript that you can access online as proof.