Noncentrosymmetric (NCS) phases are seldom seen in layered A(2)BO(4) Ruddlesden Popper (214 RP) oxides. In this work, we uncover the underlying crystallographic symmetry restrictions that enforce the spatial parity operation of inversion and then subsequently show how to lift them to achieve NCS structures. Simple octahedral distortions alone, while impacting the electronic and magnetic properties, are insufficient. We show using group theory that the condensation of two distortion modes, which describe suitable symmetry unique octahedral distortions or a combination of a single octahedral distortion with a "compositional" A or B cation ordering mode, is able to transform the centrosymmetric aristotype into a NCS Structure. With these symmetry guidelines, we formulate a data-driven model founded on Bayesian inference that allows us to rationally search for combinations of A- and B-site elements satisfying the inversion symmetry lifting criterion. We describe the general methodology and apply it to 214 iridates with A(2+) cations, identifying RP-structured Ca2IrO4 as a potential NCS oxide, which we evaluate with density functional theory. We find a strong energetic competition between two closely related polar and nonpolar low-energy crystal structures in Ca2IrO4 and suggest pathways to stabilize the NCS structure.