The dynamics triggered by the impact of an ion onto a solid surface has been explored mainly by theoretical modeling or computer simulation to date. Results indicate that the microscopic nonequilibrium relaxation processes triggered by the interaction of the ion with the solid occur on (sub)picosecond time scales. A suitable experimental approach to these dynamics therefore requires a pump-probe method with an appropriate time resolution. Recent experiments have successfully used laser photoionization of noble gas atoms in combination with a Wiley-MacLaren ion buncher to obtain arrival time distributions as narrow as t_ion=180 ps. Here, we show that this setup can be significantly improved by replacing the gas at a temperature of T_atoms≃300 K with a supersonic beam of cooled noble gas atoms at T_atoms≃4 K. The detailed analysis of measured arrival times of individual Ne⁺ ions with a kinetic energy of 4 keV reveals that the arrival time jitter can be reduced by this technique down to (18±4) ps. This opens the door to pump-probe experiments with keV ions with a time resolution in the picosecond range.