  The origin of calcium production in the first stars (Pop III stars), which
formed out of the primordial matter of the Big Bang, and their fates, remain
most fascinating mysteries in astrophysics. Advanced nuclear burning and
supernovae were thought to be the dominant source of the Ca production seen in
all stars. Here we report on a qualitatively different path to Ca production
through break-out from the "warm" carbon-nitrogen-oxygen (CNO) cycle. We extend
direct measurement of the $^{19}$F($p$, $\gamma$)$^{20}$Ne break-out reaction
down to an unprecedentedly low energy point of 186 keV and discover a key
resonance at 225 keV. In the domain of astrophysical interest, at around 0.1
giga kelvin, this thermonuclear $^{19}$F($p$,$\gamma$)$^{20}$Ne rate is up to a
factor of 7.4 larger than the previous recommended rate. Our stellar models
show a stronger break-out during stellar hydrogen burning than thought before,
and may reveal the nature of Ca production in Pop III stars imprinted on the
oldest known ultra-iron poor star, SMSS0313-6708. This result from the China
Jinping Underground Laboratory, the deepest laboratory in the world, offering
an environment with extremely low cosmic-ray induced background, has
far-reaching implications on our understanding of how the first stars evolve
and die. Our rate showcases the impact that faint Pop III star supernovae can
have on the nucleosynthesis observed in the oldest known stars and first
galaxies, key mission targets of the James Webb Space Telescope.
