Global trade flows and supply chains adjust gradually. Empirical estimates of the trade elasticity for the short run are about half as large as those for the long run and suggest that trade is subject to substantive adjustment frictions. We develop a tractable framework that provides microfoundations for dynamic trade adjustment. The model features staggered sourcing decisions, nests the Eaton-Kortum model as the limiting long-run case, and rationalizes reduced-form estimation of horizon-specific trade elasticities. We calibrate the model to horizon-specific trade elasticities and use it to quantify the welfare impact of the 2018 US-China trade war. Staggered sourcing decisions considerably exacerbate losses from the trade war, with cumulative welfare losses 300% larger in the short run and 70% larger in the long run than in the Eaton-Kortum benchmark. Third countries such as Mexico can suffer welfare losses in the short run and welfare gains in the long run.