  Abbreviated. We aim to identify new low-mass companions to young stars using
the astrometric measurements provided by the Gaia space mission and
complementary VLT/SPHERE data. We identify companion candidates from a sample
of K-type, pre-main sequence stars in the Scorpius Centaurus association using
the early version of the third data release of the Gaia space mission. Based on
the provided positions, proper motions, and magnitudes, we identify all objects
within a predefined radius whose differential proper motions are consistent
with a gravitationally bound system. We derive companion masses through
comparison with evolutionary tracks. For seven identified companion candidates
we use additional data collected with VLT/SPHERE and VLT/NACO to assess the
accuracy of the properties of the companions based on Gaia photometry alone. We
identify 110 comoving companions that have a companionship likelihood of more
than $95\,\%$. We identify ten especially intriguing companions that have
masses in the brown dwarf regime down to $20\,M_\mathrm{Jup}$. Our
high-contrast imaging data confirm both astrometry and photometric masses
derived from Gaia alone. We discover a new brown dwarf companion, TYC
8252-533-1 B, with a projected separation of approximately $570\,\mathrm{au}$
from its Sun-like primary. SED modeling provides a companion mass of
$52^{+17}_{-11}\,M_\mathrm{Jup}$. We show that the Gaia database can identify
low-mass companions at wide separations from their host stars. For K-type
Sco-Cen members Gaia can detect sub-stellar objects at projected separations
larger than $300\,\mathrm{au}$ and is sensitivity limited beyond
$1,000\,\mathrm{au}$ with a lower mass limit down to $20\,M_\mathrm{Jup}$. A
similar analysis of other star-forming regions could significantly enlarge the
sample size of such objects and test formation and evolution theories of
planetary systems.
