Sediment layer chronology
In simple big picture terms, Sediments were deposited first from the bottom upwards (as you understand). Then the area was uplifted and the river eroded from the top down.

Most erosion is from the top down (there are scenarios such as dissolution and caves which are relatively rare exceptions). So here in Texas we find a large amount of the center of the state was covered with Cretaceous sediments which have since eroded away. We see signs of this from "outliers" - basically remnant caps of Cretaceous on the tops of hills.

As I say this is big picture viewpoint. The very bottom of the Grand Canyon has metamorphic rocks. And sedimentation will not have been continuous. There are gaps from erosion, uplift, etc. But yes the bottom is about 2 billion years old, and erosion of the canyon itself is "relatively" recent.