We investigate the turn-on process in a laser cavity where the round-trip time is several orders of magnitude greater than the active medium timescales. In this long delay limit, we show that the universal evolution of the photon statistics from thermal to Poissonian distribution involves the emergence of power dropouts. While the largest number of these dropouts vanish after a few round-trips, some of them persist and seed coherent structures similar to dark solitons or Nozaki-Bekki holes described by the complex Ginzburg-Landau equation. These coherent structures connect stationary laser emission domains having different optical frequencies. Moreover, they emit intensity bursts which travel at a different speed, and, depending on the cavity dispersion sign, they may collide with other coherent structures, thus leading to an overall turbulent dynamics. The dynamics is well-modeled by delay differential equations from which we compute the laser coherence time evolution at each round-trip and quantify the decoherence induced by the collisions between coherent structures.