The conditions for the mild initiation of the detonation of homogeneous stoichiometric ethylene-oxygen mixtures diluted with nitrogen up to similar to 40%vol. in a planar semi-confined slit-type combustor with a slit 5.0 +/- 0.4 mm wide, simulating the annular combustor of a Rotating Detonation Engine (RDE), are determined experimentally using self-luminous high-speed video recording and pressure measurements. To ensure the mild detonation initiation, the fuel mixture in the RDE combustor must be ignited upon reaching a certain limiting (minimal) fill with the mixture and the arising flame must be transformed to a detonation via deflagration-to-detonation transition (DDT). Thus, for mild detonation initiation in a C2H4 + 3O(2) mixture filling the slit, the height of the mixture layer must exceed the slit width by approximately 10 times (similar to 50 mm), and for the C2H4 + 3(O-2 + 2/5 N-2) mixture, by approximately 60 times. The limiting height of the mixture layer required for DDT exhibits a sharp increase at a nitrogen-to-oxygen mole ratio above 0.25. Compared to the height of the detonation waves continuously rotating in the RDE combustor in the steady-state operation mode, for a mild start of the RDE, the fill of the combustor with the explosive mixture to a height of at least four times more is required.