  $Gaia$ BH1, the first quiescent black hole (BH) detected from $Gaia$ data,
poses a challenge to most binary evolution models: its current mass ratio is
$\approx{0.1}$, and its orbital period seems to be too long for a post-common
envelope system and too short for a non-interacting binary system. Here, we
explore the hypothesis that $Gaia$ BH1 formed through dynamical interactions in
a young star cluster (YSC). We study the properties of BH-main sequence (MS)
binaries formed in YSCs with initial mass $3\times{}10^2-3\times{}10^4$
M$_\odot$ at solar metallicity, by means of $3.5\times{}10^4$ direct $N$-body
simulations coupled with binary population synthesis. For comparison, we also
run a sample of isolated binary stars with the same binary population synthesis
code used in the dynamical models. We find that BH-MS systems that form via
dynamical exchanges populate the region corresponding to the main orbital
properties of $Gaia$ BH1 (period, eccentricity, and masses). In contrast, none
of our isolated binary systems matches the orbital period and MS mass of $Gaia$
BH1. Our best matching $Gaia$ BH1--like system forms via repeated dynamical
exchanges and collisions involving the BH progenitor star, before it undergoes
core collapse. YSCs are at least two orders of magnitude more efficient in
forming $Gaia$ BH1--like systems than isolated binary evolution.
