Note that Platonism and Aristotelianism date to around the 4th century BCE, and the Hellenistic schools date to around the 3rd century BCE, whereas the, first, toleration, and, second, official acceptance of Christianity by the Roman state occurred in the 4th century CE. So we're talking a span of eight centuries between Plato being "groundbreaking" and the acceptance of Christianity, which is a bit long to be characterized as "all of a sudden." This is like saying, "How come we built the Chartres Cathedral and then all of a sudden Taylor Swift is making an alt-folk album?"

If we set aside the comparison to groundbreaking schools of Greek philosophy, there's still about three and a half centuries between founding events in Christianity like the Council of Jerusalem and the adoption of Christianity as the Roman religion, and that includes periods of considerable suppression of the Christian population. So again there's something considerably more drawn out than an "all of a sudden" shift and adoption of Christianity here.

Note also that the characterization that this shift involved "ditch[ing] all of this and basically convert[ing] to a new way of thinking" is quite inapt. There is a certainly an important cultural shift between pagan Greco/Roman culture and Christian late antique/medieval culture, but it's not one of ditching everything and starting fresh on something new. Christian culture generally saw itself preserving and continuing the inquiries of, as they saw it, the best of Greco-Roman intellectual culture. This connection is exhibited both in the intellectual content of the relevant thinking -- formative Christian thinkers like Augustine and Eriugena among the Latins and the Cappadocians, Pseudo-Dionysius, and Maximus the Confessor among the Greeks were deeply and self-consciously indebted to their studies of the Greco-Roman schools, and Platonism in particular -- and in institutional projects like Boethius' attempt to preserve the study of Aristotle through a set of Latin translations.

Neither is it clear that the issue of monotheism is particularly relevant here. There are significant interpretive disputes about how to interpret the technical details of Greco-Roman philosophical theology, but the traditional view finds important and native monotheist traditions in ancient Greco-Roman thought dating back to the beginning of philosophy in sources like Anaxagoras, Heraclitus, and, most famously, Xenophanes. Whereas one popularly thinks of the Greek gods only in terms of the Greek mythology one might have encountered in popular sources like movies and tv shows, the development of philosophy introduced new ways of thinking about theology -- and often ways that were expressly in conflict with this earlier, Homeric tradition. Insofar as there is this trend toward monotheism found in some of the Presocratics, it is continued in later schools like the Stoics -- the traditional view is that this trend is also exhibited in Plato and Aristotle, and this is still widely held, but there is at least some more ambiguity in their cases.

So I think your question stumbles somewhat in being based on some false pretenses: that there's a sudden shift between groundbreaking schools of ancient Greco-Roman thought and the acceptance of Christianity, when rather there's a span of around eight centuries to account for; that the acceptance of Christianity represents simply ditching all of ancient Greco-Roman thought, when it doesn't but rather involves considerable appropriation and ongoing development of ancient Greco-Roman sources; and that an acceptance of monotheism would be a particularly striking novelty in this context, when the philosophical tradition of theology dating back to the 6th century BCE or so is usually regard as having already done much to prepare the relevant waters.

Several days ago when you asked for sources on this in /r/askphilosophy, I recommended the two volumes of The Cambridge History of Philosophy in Late Antiquity, which covers much of the relevant developments in an encyclopedic way -- exploring, for instance, the intersection between pagan and Christian thought in late antiquity. So I'll repeat that recommendation and urge that a source like this might better address some of what I worry are false premises leading you to misconstrue how much, or in what sense, there's a problem here needing solution. Likewise, /u/as-well had addressed with you this issue of Christian culture supposedly ditching all of the pagan heritage -- and pointed you toward the chapter on Christianity in The Routledge Handbook of Neoplatonism as a corrective. So since you still seem to be thinking this way, I would urge you to consider the significance of this advice.

No doubt there is much more to be said about things like the social conditions for the expansion of Christianity, which might still suitably address significant aspects of your question. So perhaps the historians here might helpfully speak to that, or add further considerations to the present issues.