An experimental study of $omega$ photoproduction on the proton was conducted by using the Crystal Ball and TAPS multiphoton spectrometers together with the photon tagging facility at the Mainz Microtron MAMI. The $gamma ptoomega p$ differential cross sections are measured from threshold to the incident-photon energy $E_gamma=1.40$ GeV ($W=1.87$ GeV for the center-of-mass energy) with 15-MeV binning in $E_gamma$ and full production-angle coverage. The quality of the present data near threshold gives access to a variety of interesting physics aspects. As an example, an estimation of the $omega N$ scattering length $alpha_{omega p}$ is provided.