How can a Type B blood be able to make Type A antibodies if it has not been exposed to it?

Type A or Anti -A as it is known, is an inate antibody which is not produced as a result of antigenic stimulus - ie a person of blood group B is genetically encoded to produce it.  The same is true of those with Group A blood who have Anti B in their system and Group O individuals who have Anti A and Anti B in their system.  People who are of Blood group AB don't produce any inate antibody.  it is a sort of defense mechanism and explains why you cant donate certain blood groups to others ie if you give Group A blood to a Group B person who has Anti A in their system -  the Anti A antibody attacks the Group A blood and destroys it.

The body already has antibodies against type B blood antigens, only in very small amounts. The B lymphocyte with the specific membrane bound antibody will recognise the type B antigens and its proliferation and differentiation to plasma cells, which produce more antibodies against the antigen, will be activated.

that's a good question, i will answer it, but i hoep you will choose the best answer

yes the production of antibody do usually requires the host being exposed to the antigen, there one thing you might not know about the ABH blood antigen is that they are carbohydrate structure attached to protein on cell membrane with terminal structure being galactose-N-acetylglucosamine-galactose than fucose (H) or fucose with N-acetylgalatosamine (A) or galactose (B). although the person didn't expose this antigen from blood transfusion or other blood exchanging activity, but there is a source which is most likely to be the antigen source

in out guts, mouth, skin there are millions of bacteria for which their existence is benefical to us because it disallow the colonisation of other harmful bacteria, known as comensals, they dies too and digested by the blood and their dead part are released into the blood stream  for which the B-cells, and monocytes, or macrophages in the tissue to phagacytose, and as you known their baterial membrane also comprise of glycoprotein structure, glycolipid, and pollysaccharide etc, of those hetergeneous antigens, there are some for which are similar to the ABH antigen that cause cross-reaction

thus the body did exposed to the antigen (but not exactly the same) from bacterium which lives on us such as staphylacoccus areus, streptococcus etc, or some fungus too.