Non-central heavy-ion collisions contain large orbital angular momentum () that, at high energies, is expected to induce strong vorticity in the hot bulk fluid and generate global spin polarization of produced particles. As the collision energy approaches threshold, the observed global spin polarization should reach a maximum, then drop to zero as increased stopping competes with decreased initial momentum. Recent experimental measurements, however, appear to show a continual rise of hyperon polarization even down to GeV, suggesting a peak very near threshold and hard to interpret theoretically. Here, we develop a simple Glauber-based initial state model to investigate the initial distribution of angular momentum with respect to rapidity, and the dependence of this distribution on initial baryon stopping across a wide range of collisional beam energy. We estimate that the angular momentum per produced final particle at mid-rapidity peaks around 5 GeV, which presents a potential challenge to an interpretation of the spin polarization measurements near threshold as a consequence due to the initial angular momentum of the colliding system.