It has been suggested that the Galactic center region experienced a giant explosion ∼1.5 × 107 yr ago, releasing in excess of ∼1056 ergs. This energy could be due to a starburst involving more than ∼105 supernovae, or it might be due to a massive black hole at the Galactic center. The former scenario can, in principle, be tested through a search for either the resulting γ-ray lines from the production of radioactive species or a search for the radio pulsars that were injected into the Galactic gravitational field during the starburst. Because of their high space velocities pulsars, could be a useful tracer of such starburst episodes. We present an exploratory study of pulsars associated with starbursts in or near the Galactic center and argue that a dedicated radio search for these pulsars might be able to identify the signature of a starburst. Detection of pulsars from a brief and recent injection period would also provide a valuable tool for studying the gravitational potential in the Galactic bulge region. This part of the Galactic mass model is poorly understood, but has significant implications for studies of the Galactic center bar as well as observations of gravitational microlensing of stars in the bulge.