  The rate at which helium ($^4$He) and deuterium ($d$) fuse together to
produce lithium-6 ($^6$Li) and a $\gamma$ ray, $^4$He$(d,\gamma)^6$Li, is a
critical puzzle piece in resolving the roughly three orders of magnitude
discrepancy between big bang predictions and astronomical observations for the
primordial abundance of $^6$Li. The accurate determination of this radiative
capture rate requires the quantitative and predictive description of the fusion
probability across the big bang energy window ($30$ keV $\lesssim E\lesssim
400$ keV), where measurements are hindered by low counting rates. We present
first-principles (or, ab initio) predictions of the $^4$He$(d,\gamma)^6$Li
astrophysical S-factor using validated nucleon-nucleon and three-nucleon
interactions derived within the framework of chiral effective field theory. By
employing the ab initio no-core shell model with continuum to describe $^4{\rm
He}$-$d$ scattering dynamics and bound $^6\rm Li$ product on an equal footing,
we accurately and consistently determine the contributions of the main
electromagnetic transitions driving the radiative capture process. Our results
reveal an enhancement of the capture probability below 100 keV owing to
previously neglected magnetic dipole (M1) transitions and reduce by an average
factor of 7 the uncertainty of the thermonuclear capture rate between $0.002$
and $2$ GK.
