The statute of limitations is the deadline after which a lawsuit generally cannot be filed. For most California personal injury claims it is two years from the date of injury (Code of Civil Procedure §335.1). For claims against government entities — a city bus, a dangerous public road — a special administrative claim is generally required within six months.
Miss the deadline and even a strong case is usually barred entirely. There are limited exceptions (for example, when an injury is discovered later, or the injured person is a minor), but none of them are safe to assume on your own.
The practical pressure is tighter than the legal one: camera footage gets overwritten in days or weeks, witnesses move, and vehicles get repaired. Treat the two-year limit as the outer wall, not the schedule.