How is the rotation of a collapsing core observationally confirmed?

By observing a velocity gradient across the core in line-of-sight measurements

While infall confirms the vertical contraction driven by gravity, rotation must be confirmed independently, as it is a consequence of angular momentum conservation within the collapsing gas. Rotation is confirmed by measuring differences in the line-of-sight velocities across the face of the core. If the core is rotating, one side will appear to be moving toward the observer (exhibiting a blue-shift), while the opposite side will appear to be moving away (exhibiting a red-shift), relative to the core's center of mass. This difference in velocity across the spatial extent of the core—a velocity gradient—is the observational signature that confirms the existence of rotational motion, which subsequently dictates the formation of the accretion disk around the central object.