  We present extensive ultraviolet (UV) and optical photometric and optical
spectroscopic follow-up of supernova (SN)~2021gno by the "Precision
Observations of Infant Supernova Explosions" (POISE) project, starting less
than two days after the explosion. Given its intermediate luminosity, fast
photometric evolution, and quick transition to the nebular phase with spectra
dominated by [Ca~II] lines, SN~2021gno belongs to the small family of
Calcium-rich transients. Moreover, it shows double-peaked light curves, a
phenomenon shared with only four other Calcium-rich events. The projected
distance from the center of the host galaxy is not as large as other objects in
this family. The initial optical light-curve peaks coincide with a very quick
decline of the UV flux, indicating a fast initial cooling phase. Through
hydrodynamical modelling of the bolometric light curve and line velocity
evolution, we found that the observations are compatible with the explosion of
a highly-stripped massive star with an ejecta mass of $0.8\,M_\odot$ and a
$^{56}$Ni mass of $0.024~M_{\odot}$. The initial cooling phase (first light
curve peak) is explained by the presence of an extended circumstellar material
comprising $\sim$$10^{-2}\,M_{\odot}$ with an extension of $1100\,R_{\odot}$.
We discuss if hydrogen features are present in both maximum-light and nebular
spectra, and its implications in terms of the proposed progenitor scenarios for
Calcium-rich transients.
