We combine the scanning temporal ultrafast delay (STUD) technique with spin noise spectroscopy (SNS), which is based upon below band gap Faraday rotation to investigate the full temporal dynamics of stochastically orientated electron spins in slightly n-doped bulk GaAs. The application of STUD-SNS boosts the common technical bandwidth limitation of the electro-optic conversion in cw-SNS into the several hundred GHz regime. Numerical simulations highlight the strengths and examine the limitations of STUD-SNS.