The topological Kondo (TK) model has been proposed in solid-state quantum devices as a way to realize non-Fermi liquid behaviors in a controllable setting. Another motivation behind the TK model proposal is the demand to demonstrate the quantum dynamical properties of Majorana fermions, which are at the heart of their potential use in topological quantum computation. Here we consider a junction of crossed Tonks-Girardeau gases arranged in a star-geometry (forming a Y -junction), and we perform a theoretical analysis of this system showing that it provides a physical realization of the topological Kondo model in the realm of cold atom systems. Using computer-generated holography, we experimentally implement a Y-junction suitable for atom trapping, with controllable and independent parameters. The junction and the transverse size of the atom waveguides are of the order of 5 micrometers, leading to favorable estimates for the Kondo temperature and for the coupling across the junction. Since our results show that all the required theoretical and experimental ingredients are available, this provides the demonstration of an ultracold atom device that may in principle exhibit the topological Kondo effect. ; Comment: 20 pages, 3 figures. v2: main text expanded, references added