  Being motivated by recent achievements in the rapidly developing fields of
optical bound states in the continuum (BICs) and excitons in monolayers of
transition metal dichalcogenides, we analyze strong coupling between BICs in
$\rm Ta_2O_5$ periodic photonic structures and excitons in $\rm WSe_2$
monolayers. We demonstrate that giant radiative lifetime of BICs allow to
engineer the exciton-polariton lifetime enhancing it three orders of magnitude
compared to a bare exciton. We show that maximal lifetime of hybrid
light-matter state can be achieved at any point of $\mathbf{k}$-space by
shaping the geometry of the photonic structure. Our findings open new route for
the realization of the moving exciton-polariton condensates with non-resonant
pump and without the Bragg mirrors which is of paramount importance for
polaritonic devices.
