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We present a study of the white dwarf (WD) cooling sequence (CS) in the globular cluster (GC) Omega Centauri (or NGC 5139; hereafter, ω Cen), the primary goal of a dedicated Hubble Space Telescope (HST) programme. We find that the peak at the termination of the WD CS is located at mF606W = 30.1 ± 0.2 (equivalent to V ∼ 31). The brighter part of ω Cen’s WD CS is consistent with the presence of massive He-core WDs, in agreement with previous HST analyses with ultraviolet and blue filters. Comparative analyses of the WD luminosity function (LF) and theoretical counterparts show that a single-age population for the cluster is compatible with the data. However, an analysis of only the WD LF cannot entirely exclude the possibility of an age range, due to uncertainties in the present-day WD mass function, with a star formation history potentially spanning up to 5 billion years, predominantly comprising stars about 13 Gyr old, with a minority potentially as young as 8 Gyr. This underscores the need for global spectroscopic and photometric investigations that simultaneously include both the WD populations and the previous evolutionary phases, in order to fully understand the cluster’s diverse chemical compositions and ages.