  We prove that localization near band edges of multi-dimensional ergodic
random Schr\"odinger operators with periodic background potential in
$L^2(\mathbb{R}^d)$ is universal. By this we mean that localization in its
strongest dynamical form holds without extra assumptions on the random
variables and independently of regularity or degeneracy of the Floquet
eigenvalues of the background operator. The main novelty is an initial scale
estimate the proof of which avoids Floquet theory altogether and uses instead
an interplay between quantitative unique continuation and large deviation
estimates. Furthermore, our reasoning is sufficiently flexible to prove this
initial scale estimate in a non-ergodic setting, which promises to be an
ingredient for understanding band edge localization also in these situations.
