As we know, the Renaissance was celebrated as a rebirth of European art, culture, and learning, as the works of antiquity were brought into wider circulation. However, in this process, much of the learning of the Medieval Era was discarded for a variety of reasons. In some sense, there's some irony in this, as many in the Renaissance were more dogmatic in their Aristotelianism than their Medieval predecessors were, setting back many fields of intellectual discourse as scholars basically went back to basics and rebuilt their conclusions. On the other hand, it can be argued that this 'reset' fostered new ways of thinking, along different lines from Medieval scholars. I think this overall structure of viewing the Medieval era is best personified in poor Duns Scotus, a brilliant thinker who is now best remembered as the source of the word 'dunce' thanks to Renaissance Humanists.
For the sake of this discussion, we will assume that the Renaissance actually happened, and is not just a convenient label used by later scholars.
So, what if, rather than an intellectual revolution, this period of history was far more gradual and iterative? What if the scholars were more apt to see themselves as the heirs to their immediate predecessors, rather than Antiquity? Interwoven into all of this is, of course, the Protestant Reformation, so there could be some consideration as to what form it might take, but that is quite the rabbit hole, so its probably best to stay focused.
And, of course, there's the bigger question of how this could come about, which I think could be trickier. Perhaps an earlier printing press? Later fall of Constantinople? No Black Death? Earlier re-introduction of Platonic and other non-Aristotelian texts?