Thin sheets deposited on a substrate and interfaces of correlated materials offer a plethora of routes towards the realization of exotic phases of matter. In these systems, inversion symmetry is broken which strongly affects the properties of possible instabilities -- in particular in the superconducting channel. By combining symmetry and energetic arguments, we derive general and experimentally accessible selection rules for Cooper instabilities in noncentrosymmetric systems which yield necessary and sufficient conditions for spontaneous time-reversal-symmetry breaking at the superconducting transition and constrain the orientation of the triplet vector. We discuss in detail the implications for various different materials. For instance, we conclude that the pairing state in thin layers of Sr$_2$RuO$_4$ must, as opposed to its bulk superconducting state, preserve time-reversal symmetry with its triplet vector being parallel to the plane of the system. All pairing states of this system allowed by the selection rules are predicted to display topological Majorana modes at dislocations or at the edge of the system. Applying our results to the LaAlO$_3$/SrTiO$_3$ heterostructures, we find that while the condensates of the (001) and (110) oriented interfaces must be time-reversal symmetric, spontaneous time-reversal-symmetry breaking can only occur for the less studied (111) interface. We also discuss the consequences for thin layers of URu$_2$Si$_2$ and UPt$_3$ as well as for single-layer FeSe. On a more general level, our considerations might serve as a design principle in the search for time-reversal-symmetry-breaking superconductivity in the absence of external magnetic fields.
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