TL;DR
Generally you aren't ready to be senior if you haven't worked professionally for at least 5 years. It could take longer, and some people never get there. It's all about when it's no longer a gamble for management to entrust you with responsibility.
What is senior?
Who would you want to be senior if you were in charge? Someone who can handle responsibility in a way that minimizes the risk to you and your organization. After all, senior staff are who you put in charge of people and projects.
It's about responsibility and risk
How do you know someone is low risk? They demonstrate it. They show that they've been in many different difficult situations. They know the game, they know a million ways things can go wrong and how to handle those situations because they've done so. They know when to take risks and when not to. They understand and are skilled at diplomacy, office politics, conflict management, delegation--the soft skills. They've learned all this (usually the hard way), and can demonstrate so conclusively. And so they can demonstrate that they can handle responsibility without undue risk to the organization.
It's not actually about technical skill
None of this necessarily has anything to do with technical skill, though hopefully a senior also has strong technical breadth and depth (however strong delegation can often overcome shortfalls in technical abilities).
A junior is junior because they cannot demonstrate an ability to handle responsibility in a low-risk fashion. They may be a technical super-star. Though unlikely, they could even have all the soft-skills of a senior. But they're unproven. If given responsibility, they're a gamble.
It's not time-in-chair, but the two are often (loosely) correlated
So seniority is demonstrated skill handling responsibility in a low-risk fashion. It is usually correlated with years of experience, but the two are not equivalent. It's having a proven track record that you're someone the company can count on to take on responsibility. That's what a senior is.
Some numbers
Numerically speaking, it's rare to be ready to become senior with less than 5 years total professional experience. The number varies by person and some people never get there, but it typically happens at somewhere between 5 and 10 years total professional experience.