While the application of out-of-plane magnetic fields was, so far, believed to be detrimental for the formation of Majorana phases in artificially engineered hybrid superconducting-semiconducting junctions, several recent theoretical studies have found it indeed useful in establishing such topological phases 1-5. Majorana phases emerge as quantized plateaus in the magnetoconductance of the hybrid junctions based on two-dimensional electron gases (2DEG) under fully out-of-plane magnetic fields. The large transverse Rashba spin-orbit interaction in 2DEG, together with a strong magneto-orbital effect, yield topological phase transitions to nontrivial phases hosting Majorana modes. Such Majorana modes are formed at the ends of 2DEG-based wires with a hybrid superconductor-semiconductor integrity. Here, we report on the experimental observation of such topological phases in Josephson junctions, based on In0.75Ga0.25As 2DEG, by sweeping out-of-plane magnetic fields of as small as 0 < B(mT) < 100 and probing the conductance to highlight the characteristic quantized magnetoconductance plateaus. Our approaches towards (i) creation and detection of topological phases in small out-of-plane magnetic fields, and (ii) integration of an array of topological Josephson junctions on a single chip pave the ways for the development of scalable quantum integrated circuits for their potential applications in fault-tolerant quantum processing and computing.