I checked the thirteen ‘ani maamin’s” and it is ambiguous whether the belief in “torah she baal peh misinai” is one of the thirteen “ani maamin”s. It speaks about “torah Ha’ metuzyoh bejodeninu” – without specifying whether it incldues torah she baal peh.Clearly, the dating of the world is from “seder shenos olam”-a midrashic text.
in any case, spekaing about “ten thousand years’ is not ‘a priori’ kefirah in anything.
May I also pointo ut that nost of the posters probably confuse the last two “ani maamin’s and merge them into one to the detriment of logical thought.