We grind coffee to dramatically increase its surface area. Without this step, the water won’t be able to dissolve and transport soluble flavours into the cup. A finer grind will increase surface area by creating a larger number of smaller particles. A coarser grind will reduce surface area by creating a larger number of larger particles. The larger the surface area, the more flavour is available to the water, and the higher your extraction can be.
Note that we said, “can be”. A finer grind doesn’t guarantee a higher extraction. You also have to make sure the water can access all of that extra surface area. For example, a grind that’s too fine in an espresso machine will choke, reducing your extraction practically to zero.
Fresh hot water is great for dissolving coffee flavours. The first water you pour onto the coffee grinds will immediately start extracting flavour from them. As the extraction continues, and those flavours are moved into the water, it becomes less adept at dissolving more compounds. Providing the coffee grinds with fresh brewing water will increase the rate and amount of extraction (providing there are still flavour compounds left to be extracted).
In a traditional chemistry mass transfer process, the solute (coffee) is extracted multiple times with fresh additions of solvent (water). The subsequent additions of solvent have a greater capacity for flavour extraction because they are still “empty” of dissolved flavours and “hungry” for more. This effect is due to the diffusion process: soluble compounds will more readily move into a solvent that has a lower concentration of dissolved compounds.
You may find advantages in experimenting with pump pressure and flow restriction. Low pressure, from 6 bars and under, may reduce the standard deviation between shots and increase extraction rates. Wherever you change pressure, you will also change flow. Wherever you reduce flow, you increase the contact time between H2O molecules and the soluble compounds you want them to bond with.