No, an object with zero initial velocity cannot travel through space forever. In the absence of any external forces acting on the object, it will continue to move with a constant velocity. However, due to various factors and influences present in space, such as gravitational forces and the presence of other celestial bodies, the object's trajectory will likely be altered over time.
Gravitational forces from nearby celestial bodies can have an impact on the object's motion. Over long periods, these gravitational influences can cause the object to deviate from its initial path and potentially be pulled towards other objects or into orbits around them.
Additionally, interstellar gas and dust particles, though sparse, can exert a drag force on the object, causing it to gradually lose its momentum and slow down. This effect, known as interstellar drag, can eventually bring the object to a halt.
Moreover, other factors like radiation pressure from stellar sources and the potential encounters with micrometeoroids or space debris can also affect the object's trajectory and potentially lead to its eventual capture by a celestial body or expulsion from the solar system.
Therefore, even in the absence of an initial velocity, external influences and forces present in space make it unlikely for an object to travel indefinitely without any change in its trajectory.