There is no suggestion that up to that point he had supposed that in order to get to “heaven,” one had to please Israel’s God by performing good moral works, and that he was now offering an easier way (“You just have to believe!”). Both of these suggestions—widely popular in Western thought over the last few centuries—are simply anachronistic. This is not how Jews or pagans of the time were thinking, and it certainly isn’t how Paul’s mind worked.
