Conservation of momentum in a collision between particles can be understood on the basis of:

The conservation of momentum in a collision is fundamentally derived from Newton's second and third laws of motion. Newton's second law defines force as the rate of change of momentum (F = dp/dt), establishing the relationship between force and momentum. During a collision between two particles, Newton's third law states that the forces exerted by the particles on each other are equal in magnitude and opposite in direction [1]. Since these internal forces act for the same duration, the impulse (change in momentum) experienced by one particle is equal and opposite to that experienced by the other. Consequently, the total momentum of the isolated system remains constant [1]. While energy conservation is a separate fundamental principle, it is not the basis for momentum conservation, as momentum is conserved even in inelastic collisions where kinetic energy is lost.

Sources

1. [1] https://www.grc.nasa.gov/www/k-12/airplane/conmo.html