Unless what you are doing is going out to a paying customer ( if you are doing it just for yourself)
Download and use that footage as a layer.
If you need to recreate this as your original work Just make a shape layer of color with a black spot, add a gradient effect to get the nice shading
Then scale it through the range of center sizes you need and precomp that/
Use that precom to clone as many layers as you want.
There would be multiple ways to stagger them for time to get the cascade effect.
An expression can be written or modified from a web downloaded script to keep the scaling proportional over time. if you just wanted to animate shape layers.
Whether you are confident enough to animate repeated shape
layers with an expression or clone some time - scale precomped footage for layering there are many variations possible.
Starting out making a single shape laye and scaling it over time will give you a starting point to understanding how you could make it work.