We demonstrate the occurrence of a topological phase transition induced by an effective magnetic field in a two-dimensional electron gas with spin-orbit coupling and in proximity to an s-wave superconductor. The effective, perpendicular magnetic field is generated by an in plane, off-resonant ac-magnetic field or by circularly polarized light. The conditions for entering the topological phase do not rely on fine parameter tuning: For fixed frequency, one requires a minimal amplitude of the effective field which can be evaluated analytically. In this phase, chiral edge states generally emerge for a system in stripe geometry unless the Rashba and Dresselhaus coupling have the same magnitude. In this special case, for magnetic field driving the edge states become Majorana flat bands, due to the presence of a chiral symmetry; the light irradiated system is a trivial superconductor.