CUPID will be a next generation experiment searching for the neutrinoless
double $\beta$ decay, whose discovery would establish the Majorana nature of
the neutrino. Based on the experience achieved with the CUORE experiment,
presently taking data at LNGS, CUPID aims to reach a background free
environment by means of scintillating Li$_{2}$$^{100}$MoO$_4$ crystals coupled
to light detectors. Indeed, the simultaneous heat and light detection allows us
to reject the dominant background of $\alpha$ particles, as proven by the
CUPID-0 and CUPID-Mo demonstrators. In this work we present the results of the
first test of the CUPID baseline module. In particular, we propose a new
optimized detector structure and light sensors design to enhance the
engineering and the light collection, respectively. We characterized the heat
detectors, achieving an energy resolution of (5.9 $\pm$ 0.2) keV FWHM at the
$Q$-value of $^{100}$Mo (about 3034 keV). We studied the light collection of
the baseline CUPID design with respect to an alternative configuration which
features gravity-assisted light detectors' mounting. In both cases we obtained
an improvement in the light collection with respect to past measures and we
validated the particle identification capability of the detector, which ensures
an $\alpha$ particle rejection higher than 99.9%, fully satisfying the
requirements for CUPID.