<p>Canonical typicality is a fundamental notion in quantum statistical physics, which demonstrates that in a bipartite system, the reduced state of the small subsystem is overwhelmingly close to the maximally mixed state. In this work, we study canonical typicality of random tensor networks on the two-dimensional spin lattice. Namely, we introduce a natural Gaussian sampling scheme for translation-invariant random projected entangled pair states (PEPS), motivated by recent work of Lancien and Pérez-García. Using tools from random matrix theory together with concentration-of-measure phenomena for Gaussian ensembles, we show canonical typicality for these random PEPS. Our results extend the seminal work of Collins, González-Guillén, and Pérez-García on random matrix product states (MPS) to the setting of two-dimensional lattice models and provide a mathematical foundation for understanding thermalization-like behavior in higher-dimensional tensor network states.</p>