Your
career change plans make good sense (in the brief case you made in your write-up!). And you’re right that people do transition into MC from a wide array of fields. Some ways to strengthen your case further are (a) to demonstrate knowledge of your target new industry and function, even though you don’t have hands-on experience with them, and (b) show how the skills and knowledge gained from your career to date are relevant and will enable you to contribute in your future career.
I do not think it is too early – you can clearly make your case for “why now.”
As for your bank not being a known entity to the adcoms – they actually may know it if it’s top in your country. But you’re right not to assume their knowledge – take the opportunity in each application, in the online form and/or the essays, to clarify the bank’s stature in your country. After all, many MBA applicants have to do this; it’s not a negative point, you just have to take on the onus of ensuring adcoms understand.