How does a soiless mix become soil?

How does a soiless mix become soil?

Let's say we have a clay type of soil.
We put a 12" tall raised bed on it.
We till some compost into the clay soil to create a more gradual transition.
We fill the raised bed with equal parts: compost, sand, coco/moss.

If soil is made up of aggregates, how does the clay at the bottom reach the mix at the top to form an aggregate?
Like... how does the top 3" or 6" of the raised bed ever contain or become a nice loamy soil?

The short answer is that soil life like worms  will pull mulch or other surface amendments down with them as they feed on it. The more appealing the mulch is to that soil life as food and shelter, the faster it will be integrated into the soil. Water will also carry organic matter down with it.