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We study the starting up phase of a current-controlled oscillator based on a magnetic vortex orbiting around a nanocontact in a spin-valve. From the idle state, current pulses down to a few nanoseconds can create the vortex, which is detected through the electrical signature of its steady-state gyration. Two ns are needed to reach the in-current equilibrium. The process can then be described by an Arrhenius law, with an activation energy that is consistent with the Oersted-field-induced separation of a vortex-antivortex pair. Requirements for deterministic nucleation are deduced, with prospects for instant-on oscillator capability.