I guess everyone knows Plato's allegory of the cave. He assumes people are in caves and then, he suggests that there is a possibility of "going out of the caves", gaining several nice properties with this. Do we have evidence that he noticed that we could "get out of a cave" and still be inside another "cave"? And that there could be an arbitrary number of nested caves?
That is your proposition and not Plato's. But I have to tell you the rule of the cosmos, that is "There is beginning, there is intermediate, and there is the end". One has begun to achieve the end trough intermediates. In fact, there is no continuity just as you want it to be in an infinite process, but this process of getting out of the darkness and reaching the light happens in everything and in every moment, therefore you never get out of the cave to enter another cave, although you may have come out of the cave a thousands of times.