  Triangular Heisenberg antiferromagnets are prototypes of geometric
frustration, even if for nearest-neighbor interactions quantum fluctuations are
not usually strong enough to destroy magnetic ordering: stronger frustration is
required to stabilize a spin-liquid phase. On the basis of static magnetization
and electron spin resonance measurements, we demonstrate the emergence of
${\tilde{j}_{\text{eff}}=\frac12}$ moments in the triangular-lattice magnet
Na$_2$BaCo(PO$_4$)$_2$. These moments are subject to an extra source of
frustration that causes magnetic correlations to set in far above both the
magnetic ordering and Weiss temperatures. Corroborating the
$\tilde{j}_{\text{eff}}=\frac12$ ground state, theory identifies ferromagnetic
Kitaev exchange anisotropy as additional frustrating agent, altogether putting
forward Na$_2$BaCo(PO$_4$)$_2$ as a promising Kitaev spin-liquid material.
