You know how far away they were because energy is conserved. Even if they stick together completely after attracting, the internal energy of these particles must be increased. Quantum-mechanically, this means the system ends up in an excited state after collision, and radiates this energy away after some time. By measuring this radiation, you get information about the initial conditions.

You know how far away they were because energy is conserved. Even if they stick together completely after attracting, the internal energy of these particles must be increased. You can measure the internal energy of these particles through, say, measuring their temperature (via their blackbody spectrum or something similar). Therefore, you can determine how much energy was involved in the collision.

You can also determine the impact parameter of the collision (and also the plane in which the collision occurred) by measuring the angular momentum of the final system. The velocity of the center of mass gives you the sum of the initial momenta. The phase of the rotation of the system then gives you the particles' initial direction of approach, which means you can completely reconstruct the initial conditions.