  In this paper, we consider the stochastic Boussinesq equations on $\mathbb
T^3$ with transport noise and rough initial data. We first prove the existence
and uniqueness of the local pathwise solution with initial data in
$L^p(\Omega;L^p)$ for $p>5$. By assuming additional smallness on the initial
data and the noise, we establish the global existence of the pathwise solution.
