An intense positron sources is a demanding element in the design of future lepton colliders. A crystal-based hybrid positron source could be an alternative to a more conventional scheme based on the electron conversion into positron in a thick amorphous target. The conceptual idea of the hybrid source is to have two separate objects, a photon radiator and a photon-to-positron converter target. In such a scheme an electron beam crosses a thin axially oriented crystal with the emission of a channeling radiation, characterized by a considerably larger amount of photons if compared to Bremsstrahlung. The net result is an increase in the number of produced positrons at the converter target. In this paper we present the results of a beam test conducted at the DESY TB 21 with 5.6 GeV electron beam and a crystalline tungsten radiator. Experimental data clearly highlight an increased production of photons and they are critically compared with the outcomes of novel method to simulate the number of radiated photons, showing a very good agreement. Strong of this, the developed simulation tool has been exploited to design a simple scheme for a positron source based on oriented crystal, demonstrating the advantages in terms of reduction of both deposited energy and the peak energy deposition density if compared to conventional sources. The presented work opens the way for a realistic and detailed design of a hybrid crystal-based positron source for future lepton colliders.