  Our current understanding of the cosmic star formation history at z>3 is
primarily based on UV-selected galaxies (i.e., LBGs). Recent studies of
H-dropouts have revealed that we may be missing a large proportion of star
formation that is taking place in massive galaxies at z>3. In this work, we
extend the H-dropout criterion to lower masses to select optically dark/faint
galaxies (OFGs), in order to complete the census between LBGs and H-dropouts.
Our criterion (H> 26.5 mag & [4.5] < 25 mag) combined with a de-blending
technique is designed to select not only extremely dust-obscured massive
galaxies but also normal star-forming galaxies. In total, we identified 27 OFGs
at z_phot > 3 (z_med=4.1) in the GOODS-ALMA field, covering a wide distribution
of stellar masses with log($M_{\star}$/$M_{\odot}$) = 9.4-11.1. We find that up
to 75% of the OFGs with log($M_{\star}$/$M_{\odot}$) = 9.5-10.5 were neglected
by previous LBGs and H-dropout selection techniques. After performing stacking
analyses, the OFGs exhibit shorter gas depletion timescales, slightly lower gas
fractions, and lower dust temperatures than typical star-forming galaxies.
Their SFR_tot (SFR_ IR+SFR_UV) is much larger than SFR_UVcorr (corrected for
dust extinction), with SFR_tot/SFR_UVcorr = $8\pm1$, suggesting the presence of
hidden dust regions in the OFGs that absorb all UV photons. The average dust
size measured by a circular Gaussian model fit is R_e(1.13 mm)=1.01$\pm$0.05
kpc. We find that the cosmic SFRD at z>3 contributed by massive OFGs is at
least two orders of magnitude higher than the one contributed by equivalently
massive LBGs. Finally, we calculate the combined contribution of OFGs and LBGs
to the cosmic SFRD at z=4-5 to be 4 $\times$ 10$^{-2}$ $M_{\odot}$
yr$^{-1}$Mpc$^{-3}$, which is about 0.15 dex (43%) higher than the SFRD derived
from UV-selected samples alone at the same redshift.
