Summary: The Common Correlated Effects (CCE) methodology is now well established for the analysis of factor-augmented panel data models. Yet, it is often neglected that the pooled variant is biased unless the cross-section dimension \((N)\) of the dataset dominates the time series length \((T)\). This is problematic for inference with typical macroeconomic datasets, where \(T\) is often equal or larger than \(N\). In response, we establish in this paper the theoretical foundation of the cross-section (CS) bootstrap for inference with CCE estimators in large \(N\) and \(T\) panels with \(TN^{-1}\to\tau<\infty\). This resampling scheme is often used to estimate standard errors, yet without theoretical justification, and with unused potential, as we show it also provides a solution to the bias problem. We derive conditions under which the scheme replicates the distribution of the CCE estimators, such that bias can be eliminated and asymptotically valid inference can ensue. In so doing, we also spend attention to the case where factors need not be common across the dependent and explanatory variables, or when slopes are heterogeneous. Since we find that the CS-bootstrap applies in each case, researchers can stay agnostic on these issues. Simulation experiments show that the asymptotic properties also translate well to finite samples.