  The $t$-PNG model introduced in Aggarwal, Borodin, and Wheeler (2021) is a
deformed version of the polynuclear growth (PNG) model. In this paper, we prove
the hydrodynamic limit of the model using soft techniques. One key element of
the proof is the construction of a colored version of the $t$-PNG model, which
allows us to apply the superadditive ergodic theorem and obtain the
hydrodynamic limit, albeit without identifying the limiting constant. We then
find this constant by proving a law of large numbers for the $\alpha$-points,
which generalizes Groeneboom (2001). Along the way, we construct the stationary
$t$-PNG model and prove a version of Burke's theorem for it.
