This should actually be what you want in MySQL:
UPDATE wp_post
SET post_content = CONCAT(REPLACE(LEFT(post_content, INSTR(post_content, 'A')), 'A', 'B'), SUBSTRING(post_content, INSTR(post_content, 'A') + 1));
It's slightly more complicated than my earlier answer - You need to find the first instance of the 'A' (using the INSTR function), then use LEFT in combination with REPLACE to replace just that instance, than use SUBSTRING and INSTR to find that same 'A' you're replacing and CONCAT it with the previous string.
See my test below:
SET @string = 'this is A string with A replace and An Answer';
SELECT @string as actual_string
, CONCAT(REPLACE(LEFT(@string, INSTR(@string, 'A')), 'A', 'B'), SUBSTRING(@string, INSTR(@string, 'A') + 1)) as new_string;
Produces:
actual_string new_string
--------------------------------------------- ---------------------------------------------
this is A string with A replace and An Answer this is B string with A replace and An Answer
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