The spontaneous rise of a wetting liquid in a capillary tube is classically described by Washburn's law: the meniscus height increases as the square root of time, a law singular for short times, where the velocity diverges. We focus here on the early dynamics of the rise of viscous liquids, and report an initial regime of constant velocity contrasting with Washburn's prediction. This is explained by considering the contact line friction at the liquid front, and confirmed by the influence of prewetting films on the tube walls, whose presence is found to speed up the rise and more generally to provide an ideal framework for quantifying the friction at contact lines.