  Implications of the string Swampland criteria for a dark energy dominated
universe, obtained by using Gaussian processes and $H(z)$ data analysis, are
discussed. In particular, the Swampland criteria for a scalar-field dark
energy, without assuming any specific form for the potential. By allowing the
Gaussian process to reconstruct the form of the potential from $H(z)$ data,
upper bounds on the second Swampland criterion (involving $|V^{\prime}|/V$) for
two different kernel functions (the squared exponential and Matern~($\nu =
9/2$) kernels) are estimated . The approach here differs from previous studies,
since the upper bound of the second Swampland criterion is derived in a
thoroughly model-independent way, without resorting to a model-to-model
comparison strategy. The analysis is performed using the latest values of
$H_{0}$ reported by the Planck and Hubble missions. Results for the estimation
of the constant of $SC2$ hint towards the possibility of getting upper bounds
well behind the estimations for the dark energy dominated universe as reported
in previous studies, which involved model-to-model comparison. Estimations from
this new approach turn to be quite sensitive and just depend on the quality of
the data and on the kernel employed. This study is a first attempt towards the
exploitation of the Swampland criteria in a model-independent way and may be
extended to involve other datasets and, also, in trying to understand what is
the impact of higher-redshift data on the upper bounds. In the analysis,
$40$-point $H(z)$ data have been used, consisting of a $30$-point sample
deduced from a differential age method and an additional $10$-point sample
obtained from the radial BAO method. Hints towards the possibility of
eventually disproving the Swampland conjecture are noted.
