This is a solved problem in the Netherlands with iDEAL. Go to checkout, select your bank, authenticate at your banks website with your credentials and 2FA (SMS/EMV CAP reader/QR code), confirm transaction details and you'll be redirected back to the web store. The wire transfer is not instant but it is guaranteed so the merchant can start shipping immediately.
See https://www.ideal.nl/demo/en/ for a demo.