In this article, the concept of a recently funded R&D project for the installation of a proof-of-concept cavity-based x-ray free electron laser (CBXFEL) demonstrator experiment at the European XFEL facility is presented, with the first results expected in 2024. It is composed of an x-ray cavity design in backscattering geometry with a 133 m round trip length using cryogenically cooled diamond crystals. It employs the concept of retroreflection to reduce the sensitivity to vibrations. The FEL radiation is produced in four undulator segments of 20 m total length. Simulations at 16 GeV beam energy and 250 pC bunch charge show that the expected x-ray pulses in saturation surpass state-of-the-art x-ray sources considering spectral flux and three-dimensional coherence. However, the stability of the proof of concept setup is severely challenged by the finite thermal transport in the diamond crystals. Therefore, suitable measures such as cooling the crystals to 70 K are explained in this paper and additional ones will have to be developed in the course of this project.