gleam - appear briefly; "A terrible thought gleamed in her mind"

fulminate - come on suddenly and intensely; "the disease fulminated"

occur - to be found to exist; "sexism occurs in many workplaces"; "precious stones occur in a large area in Brazil"

climb - improve one's social status; "This young man knows how to climb the social ladder"

leapfrog - progress by large jumps instead of small increments

develop - grow, progress, unfold, or evolve through a process of evolution, natural growth, differentiation, or a conducive environment; "A flower developed on the branch"; "The country developed into a mighty superpower"; "The embryo develops into a fetus"; "This situation has developed over a long time"