  We explore celestial amplitude corresponding to $2d$ bulk
$\mathcal{S}$-matrix. We consider scalar particles with identical mass and show
that the celestial amplitude becomes the fourier transform of the $2d$
$\mathcal{S}$-matrix written in the rapidity variable. We translate the
crossing and unitarity conditions into the conditions on the celestial
amplitude. For the $2d$ Sinh-Gordon model, we calculate the celestial amplitude
perturbatively in coupling constant and check that the crossing and unitarity
conditions are satisfied for the celestial amplitude. Imposing the crossing and
unitarity conditions to the celestial amplitude, we want to find amplitudes to
the higher order in perturbation theory from the lower order i.e., to provide a
"\textit{proof of principle}" to show we can apply the bootstrap idea to the
celestial amplitude. We find that imposing the crossing and unitarity
conditions is not enough for bootstrapping celestial amplitude, there is an
extra term which can't be fixed by the crossing and unitarity conditions. We
also study the gravitational dressing condition in $2d$ QFT for massless
particles in celestial space and see that for the gravitationally dressed
celestial amplitude, the poles on the right half-plane get erased for several
ansatzes.
