We have analyzed a sample of 574 Spitzer 4.5 pm selected galaxies with [4.5] \textless 23 and K-s(auto) \textgreater 24 (AB) over the UltraVISTA ultradeep COSMOS field. Our aim is to investigate whether these mid-infrared (mid-IR) bright, near-infrared (near-IR) faint sources contribute significantly to the overall population of massive galaxies at redshifts z \textgreater= 3. By performing a spectral energy distribution (SED) analysis using up to 30 photometric bands, we have determined that the redshift distribution of our sample peaks at redshifts Z approximate to 2.5-3.0, and similar to 32% of the galaxies lie at z \textgreater= 3. We have studied the contribution of these sources to the galaxy stellar mass function (GS1VIF) at high redshifts. We found that the [4.5] \textless 23, K-s(auto) \textgreater 24 galaxies produce a negligible change to the GSMF previously determined for K-s(auto) \textless 24 sources at 3 \textless=, z \textless 4, but their contribution is more important at 4 \textless, z \textless 5, accounting for \textgreater50% of the galaxies with stellar masses M-st greater than or similar to 6 x 10(10) M-circle dot. We also constrained the GSMF at the highestmass end (M-st greater than or similar to 2 x 10(11) M-circle dot) at z 5. From their presence at 5 \textless= z \textless= 6 and virtual absence at higher redshifts, -st we can pinpoint quite precisely the moment of appearance of the first most massive galaxies as taking place in the similar to 0.2 Gyr of elapsed time between Z similar to 6 and Z similar to 5. Alternatively, if very massive galaxies existed earlier in cosmic time, they should have been significantly dust-obscured to lie beyond the detection limits of current, largearea, deep near-IR surveys.