Stratospheric sulfate aerosol injection (SAI) has been proposed as a way to geoengineer climate. While swift global mean surface cooling is generally expected from tropical SAI, the regional impacts of such perturbation on near‐surface air temperature (SAT) are projected to be spatially inhomogeneous. By using existing simulations from the Geoengineering Model Intercomparison Project G4 scenario, where 5 Tg/year of sulfur dioxide (SO₂) is injected into the tropical stratosphere to offset some of the warming in a midrange representative greenhouse gas concentration pathway (RCP4.5) between 2020 and 2070, we examine the regional detectability of the SAI surface cooling effect and attempt to find the best spatial scale for potential SAI monitoring. We use optimal fingerprint detection and attribution techniques to estimate the time horizon over which the SAI surface cooling effect would be detected after implementation in 2020 on subglobal scales, ranging from the near‐global in situ observational coverage down to subcontinental regions. We show that using the spatiotemporal SAT pattern across the Northern and Southern extratropics and the Tropics, and across the Northern and Southern Hemispheres, as well as averaging SATs over the whole globe robustly result in successful SAI detection within 10 years of geoengineering implementation in a majority of the included plausible geoengineering realizations. However, detecting the SAI effect on SAT within the first decade of implementation would be more challenging on subcontinental scales.