Straight out of school, yes. With a few years of outside experience and an advanced degree, it is easy to join at L5. Which I think is ideal, no promotion headaches, just focus on interesting work (L6 already starts to be management heavy, so not that attractive).
Yes switching jobs is often a path to "sideways promotion". You have to interview well, but that's something that's learnable - and more under your control in a way, than getting good promotable projects at your current employer.
