The ultrafast injection of spins and manipulation of magnetism by laser light offers a revolution in the speed of magnetic data storage. Here fully $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculation show that the flow of spin current from a ferromagnet to a nonmagnetic substrate in a spintronic device plays a crucial role in controlling laser-induced femtosecond spin dynamics. This highlights that substrate engineering can be used for precise control of early-time magnetization dynamics, thereby opening a path to material design for efficient spin injection in magnetic memory devices.