When I look up the org chart, the people higher up have been at the company 5+ years. Moving into the higher roles requires the right opportunity, which often takes time to find. Those "right opportunities" are rarely given to people new to the company and are often used to retain existing high performers.
Certainly if you're stuck in your career and are not on a growth path, jump ship. But if your job is promoting you consistently every 2–3 years, then I'd stay.