  In this paper, we initiate the study of the 2d F-theory landscape based on
compact elliptic Calabi-Yau fivefolds. In particular, we determine the boundary
models of the landscape using Calabi-Yau fivefolds with the largest known Hodge
numbers $h^{1,1}$ and $h^{4,1}$. The former gives rise to the largest geometric
gauge group in the currently known 2d (0,2) supergravity landscape, which is
$E_8^{482\,632\,421}\times F_4^{3\,224\,195\,728}\times
G_2^{11\,927\,989\,964}\times SU(2)^{25\,625\,222\,180}$. Besides that, we
systematically study the hypersurfaces in weighted projective spaces with small
degrees, and check the gravitational anomaly cancellation. Moreover, we also
initiate the study of singular bases in 2d F-theory. We find that orbifold
singularities on the base fourfold have non-zero contributions to the
gravitational anomaly.
