  Using numerical bootstrap method, we determine the critical exponents of the
minimal three-dimensional $\mathcal{N}=1$ superconformal field theory (SCFT) to
be $\eta_{\sigma}=0.168888(60)$ and $\omega=0.882(9)$. The model was argued in
arXiv:1301.7449 to describe a quantum critical point (QCP) at the boundary a
$3+1$D topological superconductor. More interestingly, the QCP can be reached
by tuning a single parameter, where supersymmetry (SUSY) is realised as an
emergent symmetry. By imposing emergent SUSY in numerical bootstrap, we find
that the conformal scaling dimension of the real scalar operator $\sigma$ is
highly restricted. If we further assume the SCFT to have only two time-reversal
parity odd relevant operators, $\sigma$ and $\sigma'$, we find that allowed
region for $\Delta_{\sigma}$ and $\Delta_{\sigma'}$ becomes an isolated island.
The result is obtained by considering not only the four point correlator
$\langle \sigma \sigma \sigma \sigma \rangle$, but also $\langle \sigma
\epsilon \sigma \epsilon \rangle$ and $\langle \epsilon \epsilon\epsilon
\epsilon \rangle$, with $\epsilon \sim \sigma ^2$ being the superconformal
descendant of $\sigma$.
