The nature of the GeV gamma-ray Galactic center excess (GCE) in the data of Fermi-LAT is still under investigation. Different techniques, such as template fitting and photon-count statistical methods, have been applied in the past few years in order to disentangle between a GCE coming from sub-threshold point sources or rather from diffuse emissions, such as the dark matter annihilation in the Galactic halo. A major limit to all these studies is the modeling of the Galactic diffuse foreground, and the impact of residual mis-modeled emission on the results' robustness. We combine for the first time adaptive template fitting and pixel-count statistical methods in order to assess the role of sub-threshold point sources to the GCE, while minimizing the mis-modelling of diffuse emission components. We reconstruct the flux distribution of point sources in the inner Galaxy well below the Fermi-LAT detection threshold, and measure their radial and longitudinal profiles. We find that point sources and diffuse emission from the Galactic bulge each contributes about 10\% of the total emission therein, disclosing a sub-threshold point-source contribution to the GCE.