Why do grasses and weeds appear before trees and shrubs?

That their roots tend to be fibrous and that they mature to a lower height are reasons why shrubs grow before trees.

Specifically, shrubs tend to have fibrous roots that grow closer to the surface and that work their way into air and moisture pore spaces in the soil. This permits shrubs to access available moisture and nutrients shortly after their entry into the soil. This means that shrubs tend to access what they need for growth before trees do. Additionally, shrubs have lower requirements in terms of mature size. Shrub heights below 30 feet (9.14 meters) are reached sooner than those above that level, which is the bottom range in mature sizes for trees.