In this paper we confront the color glass condensate and saturation approach of Contreras et al. [Non-linear equation in the re-summed next-to-leading order of perturbative QCD: The leading twist approximation, Eur. Phys. J. C 80, 1029 (2020)] with the experimental combined HERA data and obtain its parameters. The model includes two features that are in accordance with our theoretical knowledge of deep inelastic scattering. These consist of: (i) the use of analytical solution for the nonlinear Balitsky-Kovchegov evolution equation and (ii) the exponential behavior of the saturation momentum on the impact parameter b-dependence, characterized by Qs proportional to exp (-mb) which reproduces the correct behavior of the scattering amplitude at large b in accord with Froissart theorem. The model results are then compared to data at small-x for the structure function of the proton F2, the longitudinal structure function FL, the charm 2 , the exclusive vector meson (J/psi, phi, rho) production and deeply virtual Compton scattering. We obtain a good agreement for the processes in a wide kinematic range of Q2 at small-x. Our results provide a strong guide for finding an approach, based on color glass condensate and saturation effective theory for high-energy QCD, to make reliable predictions from first principles and for forthcoming experiments like the Electron Ion Collider and the LHeC.