By 'taken literally,' I assume you mean accepted as historic rather than mythical. You also speak of it 'making a jump.' It did not. Christianity was presented as being historical from the beginning. That was part of its novelty. The dying and rising God of Christianity had actually died and arisen in the immediate past of the first Christians.
The people who were initiated into the mysteries were generally not the same people as became Christians in the Roman empire. To be accepted into a mystery religion, the person had to be of good character, and of good class. Slaves and the underclasses were not admitted. That was another novelty of Christianity. It accepted slaves and underclasses. So most of the people who sought salvation through Christianity were offered no alternatives. Today we would say that Christianity exploited a market opportunity. The people who entered therefore were largely uneducated and illiterate. They were tricked because they were offered a bogus salvation putting them on a par with the rich and worthy people of society. Indeed, the Christian claim was that they were better! The last would be first and the first last.
The ones who came to it from the higher classes were at first mainly women who had already become impressed by the Jewish scriptures and their representation of God's purpose in history. Some men felt the same way about Judaism but did not like the idea of circumcision. S Paul introduced a Judaism for gentiles not requiring circumcision and which had the characteristics of the dying and rising gods. So some of the higher classes made a jump, or more aptly, a slide, into a modified Judaism that had some of the familiarity of the mysteries. It still took 300 years for Christianity to become the official Roman religion. Then it rapidly expunged its rivals with the ruthlessness that continued for centuries.