  The cosmographic approach is gaining considerable interest as a
model-independent technique able to describe the late expansion of the
universe. Indeed, given only the observational assumption of the cosmological
principle, it allows to study the today observed accelerated evolution of the
Hubble flow without assuming specific cosmological models. In general,
cosmography is used to reconstruct the Hubble parameter as a function of the
redshift, assuming an arbitrary fiducial value for the current matter density,
$\Omega_m$, and analysing low redshift cosmological data. Here we propose a
different strategy, linking together the parametric cosmographic behavior of
the late universe expansion with the small scale universe. In this way, we do
not need to assume any "a priori" values for the cosmological parameters, since
these are constrained at early epochs using both the Cosmic Microwave
Background Radiation (CMBR) and Baryonic Acoustic Oscillation (BAO) data. In
order to test this strategy, we describe the late expansion of the universe
using the Pad\'e polynomials. This approach is discussed in the light of the
recent $H(z)$ values indicators, combined with Supernovae Pantheon sample,
galaxy clustering and early universe data, as CMBR and BAO. We found an
interesting dependence of the current matter density value with cosmographic
parameters, proving the inaccuracy of setting the value of $\Omega_m$ in
cosmographic analyses, and a non-negligible effect of the cosmographic
parameters on the CMBR temperature anisotropy power spectrum. Finally, we found
that the cosmographic series, truncated at third order, shows a better $\chi^2$
best fit value then the vanilla $\Lambda$CDM model. This can be interpreted as
the requirement that higher order corrections have to be considered to
correctly describe low redshift data and remove the degeneration of the models.
