Computational discovery of magnetic materials remains challenging because magnetism arises from the competition between kinetic energy and Coulomb interaction that is often beyond the reach of standard electronic-structure methods. Here we tackle this challenge by directly solving the many-electron Schr"odinger equation with neural-network variational Monte Carlo, which provides a highly expressive variational wavefunction for strongly correlated systems. Applying this technique to transition metal dichalcogenide moir'e semicondutors, we predict itinerant ferromagnetism in WSe${}_2$/WS${}_2$ and an antiferromagnetic insulator in twisted $\Gamma$-valley homobilayer, using the same neural network without any physics input beyond the microscopic Hamiltonian. Crucially, both types of magnetic states are obtained from a single calculation within the $S_z=0$ sector, removing the need to compute and compare multiple $S_z$ sectors. This significantly reduces computational cost and paves the way for faster and more reliable magnetic material design.