A bank might finance a tiny house but not with a traditional home loan or mortgage.
A tiny home when financed by a bank would be considered an RV if it's on wheels and can easily be moved and it would be considered an RV due to the size of the tiny home.
A bank might give you an RV loan and finance the tiny home purchase that way.
Or you might be able to get a personal loan in the amount the tiny home costs and finance the tiny home that way as well.
Another option to finance a tiny home is if you currently own a regular home and have a mortgage on that home is to take out a home equity loan to pay for the tiny home.
Or sell your current home and buy the tiny home with the money and have some money leftover.