  We use the path integral optimization approach of Caputa, kundu, Miyaji,
Takayanagi and Watanabe to find the time slice of geometries dual to vacuum,
primary and thermal states in the $T\bar{T}$ deformed two dimensional CFTs. The
obtained optimized geometries actually capture the entire bulk which fits well
with the integrability and expected UV-completeness of $T\bar{T}$-deformed
CFTs. When deformation parameter is positive, these optimized solutions can be
reinterpreted as geometries at finite bulk radius, in agreement with a previous
proposal by McGough, Mezei and Verlinde. We also calculate the holographic
entanglement entropy and quantum state complexity for these solutions. We show
that the complexity of formation for the thermofield double state in the
deformed theory is UV finite and it depends to the temperature.
