The influence of a dark component on the first epoch of galaxy formation is analyzed by using the ages of the three oldest high-redshift galaxies known in the literature. Our results, based on a spatially flat accelerated universe driven by a "quintessence" component (p(x) = omega rho (x)), show that, if the inferred ages of these objects are correct, the first formation era is pushed back to extremely high redshifts. For the present best- fit quintessence model (Omegax = 0.7, omega < -0.6), we find a lower bound of z(f) <greater than or equal to> 7.7, whereas in the extreme case of the Lambda + cold dark matter model (omega = -1) the limit is slightly smaller (z(f) greater than or equal to 5.8). The case for open cold dark matter models has also been discussed. For Omega (m) similar or equal to 0.3, the formation redshift is restricted by zf greater than or equal to 18. As a general result, if Omega (m) greater than or equal to 0.37, these galaxies are not formed in FRW cosmologies with no dark energy since for all these cases z(f) --> infinity.