Yes and no. In a regular mechanical system with macroscopic parts, momentum can not be "hidden" to human eyes. But in other systems, momentum can be hidden. For instance, in an electromagnetic system, momentum can be transferred to the electromagnetic field, which is invisible to human eyes at most frequencies. Therefore, momentum can be "hidden" in the electromagnetic field. Let us explore this topic more in depth.
Every isolated system obeys the law of conservation of energy which states that if no energy is externally extracted or inserted into the system, its total energy will remain constant in time. For example, consider two hockey pucks sliding towards each other on ice. If you sum the kinetic (motional) energy of both pucks before they collide, you will find that it equals the sum of both energies after they collide. We can in fact use the conservation of energy along with some other information to predict what will happen in a simple collision like this.