The impulsively starting motion of a torus submerged horizontally below a free surface is studied analytically, using a small-time expansion. The torus is assumed wide, i.e., the torus radius is much larger than its initial submergence depth. A quasi-two-dimensional theory is applied. Its accuracy is checked by comparing the first-order surface elevation with slender-body theory. The hydrodynamic force and torque are investigated in the first three orders of the small-time expansion. The ratio between the cross-section radius and submergence depth is arbitrary (between 0 and 1). The general motion of the torus consists of all six degrees of freedom. Special emphasis is put on the five different leading-order nonlinear interactions that may occur between these modes: surge/heave, surge/roll, sway/roll, heave/roll, and roll/yaw. These leading-order nonlinear interactions give rise to zeroth-order forces and torques. The leading-order gravitational effects are investigated.