As a grad, it's not hard to move up. Check back in a year or two when progression is more "active". That said, I have seen many coworkers promoted and moved to positions that align with their long term goals.
Generally you can either grow into a senior dev. role where you can take up more responsibility for architectural / long term design and mentoring. Otherwise you can pick up a people leader role where you manage a team. Moving up the ranks is very much about talking with your manager and growing into a role and depends on the current circumstances of the company. There isn't really a regimented path.
As a graduate developer you "ungraduate" into a developer after a year and can move to senior developer, lead developer, team lead, principal engineer