  Einstein-Gauss-Bonnet (EGB) model is recently restudied in order to analyze
new consequences in gravitation, modifying appropriately the Einstein-Hilbert
action. The consequences in EGB cosmology are mainly geometric, with higher
order values in the Hubble parameter. In this vein this paper is devoted to
contribute with extra evidences about its pros and cons of the model from a
cosmological point of view. We start constraining the characteristic parameter,
$\alpha$, of the EGB model when a cosmological constant as the catalyst for the
acceleration is considered. The constrictions are developed at the background
cosmology using Observational Hubble Data, Baryon Acoustic Oscillations,
Supernovaes of the Ia type, Strong Lensing Systems and the recent compilation
of HII Galaxies. Additionally, we implement a statefinder analysis where we
found not only a late acceleration but also an early Universe acceleration
which is associated with the parameter $\alpha$. Based on our results of the
lensing systems, the Universe evolution never reaches a non accelerated phase,
instead it is always presented in an accelerated state, being a possible fault
that afflicts the EGB model.
