We report on the novel effect of the growing-in of optical coherence in the FMO antenna complexes. The rise of coherence, monitored by femtosecond two-pulse photon echo spectroscopy at 1.27 K, occurs within a characteristic time of 150-250 fs after impulsive excitation at the red edge of the absorption spectrum and is accompanied by strong and long-lasting oscillations. We show that this effect cannot be explained in the framework of present theories for the photon echo formation. To account for the observations, we take into consideration a finite system-bath interaction time and develop the theory beyond the Markov limit. We show that the coherence does not follow the impulsive excitation promptly, instead its time development is delayed. General expressions are obtained for the nonlinear polarization, which can also be applied for analysis of other time-resolved experiments (three-pulse photon echoes, transient grating, transient absorption etc.). Model calculations fully support our experimental observations.