The way a sound evolves in time contains a lot of timbrical information.

Different harmonics have different ADSR curves (Attack, Decay, Sustain, Release).

Above all, one cannot overstress the importance of the attack transient. There are famous experiments in psychoacoustics that show that, when deprived of their attack transient, the sounds of two different instruments may become hard to tell apart.

Personal anecdote: as a classic guitarist, it took me three years of experimentation to find the right way to cut my fingernails in order to have a better sound. The Electronic Engineer in me says that those were three years spent to look for how to improve 0.1 seconds of noise at the start of each of my notes.