Legal Question in Personal Injury in California

The law applies, or does not apply, liability based on facts - detailed facts - which if disputed go to a jury to decide what the facts truly were. A public facility is not automatically liable, nor is it automatically not liable, just because a child falls down stairs there. You can't just say a child fell and then ask if there is liability. The operator of the facility must do something wrong, or fail to do something that the law requires them to do, and that has to cause or substantially contribute to the cause of the fall. Without evaluation of all the relevant facts of the fall, it is impossible to tell if the facility did something wrong or failed to do something it was obligated by law to do. So there is no answer to your question.

If you can show they were negligent in design or maintenance, you might have a claim. You can forget about design, as the facility passed inspection when built. People fall all the time due to their own fault and carelessness. Nobody is 'liable' for that.