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Interactions between short laser pulses and electron bunches determine a wide range of accelerator applications. Finding spatiotemporal overlap between few-micron-sized optical and electron beams is critical, yet there are few routine diagnostics for this purpose. We present a method for achieving spatiotemporal overlap between a picosecond laser pulse and a relativistic sub-ps electron bunch. The method uses the transient change in optical transmission of a Ce:YAG screen upon irradiation with a short electron bunch to co-time the electron and laser beams. We demonstrate and quantify the performance of this method using an inverse Compton source comprised of a 30 MeV electron beam from an X-band linac focused to a 10 μm spot, overlapped with a joule-class picosecond Yb:YAG laser system. This method is applicable to electron beams with few-microjoule bunch energies and uses standard scintillator screens common in electron accelerators.