Riemannian geometry before semi-Riemannian geometry?

Question

I am interested in getting acquainted with semi-Riemannian geometry for application in general relativity. For this, it seems O'Neill's book is considered the "gold standard". I am acquainted with basic smooth manifold theory on the level of Tu's Introduction to Manifolds but am concerned my preparation may be inadequate. Is it recommended that the reader have an acquaintance with Riemannian geometry, e.g. the first 8 chapters of Lee's Introduction to Riemannian Manifolds, before attempting to tackle the more general semi-Riemannian geometry? Is there a compelling reason to (or not to) study Riemannian geometry first?