The ability to modulate the spin-orbit (SO) interaction is crucial for engineering a wide range of spintronics-based quantum devices, extending from state-of-the-art data storage to materials for quantum computing. The use of proximity-induced effects for this purpose may become the mainstream approach and their experimental verification using angle-resolved photoelectron spectroscopy (ARPES) has so far been elusive. Here, using the advantages of soft-X-ray ARPES on its probing depth and intrinsic resolution in three-dimensional momentum k, we identify a distinct modulation of the SO interaction in a van der Waals semiconductor (MoSe2) proximitized to a high-Z metal (Pb), and measure its variation through the k space. The strong SO field from Pb boosts the SO splitting by up to 30% at the H-point of the bulk Brillouin zone, the spin-orbit hotspot of MoSe2. Tunability of the splitting via the Pb thickness allows its tailoring to particular applications in emerging quantum devices.