The Gamma Factory (GF) initiative proposes to create novel research tools at CERN by producing, accelerating and storing highly relativistic partially stripped ion beams in the LHC rings and by exciting their atomic degrees of freedom by lasers, to produce high-energy photon beams. Their intensity would be several orders of magnitude higher than those of the presently operating light sources in the particularly interesting gamma-ray energy domain reaching up to 400 MeV. In this energy domain, the high-intensity photon beams can be used to produce secondary beams of polarized electrons, polarized positrons, polarized muons, neutrinos, neutrons and radioactive ions. Over the years 2017-2018 we have demonstrated that these partially stripped ion beams can be successfully produced, accelerated and stored in the CERN accelerator complex, including the LHC. The next step of the project is to build a proof of principle experiment in the SPS to validate the principal GF concepts. This contribution will present the initial conceptual design of this experiment along with its main challenge - the demonstration of the fast cooling method of partially stripped ion beams.