Is There a Time Limit for Applying for a 60-Day Family-Based Extension Before My Exit Date?

Is there a time limit prior to the exit date stamp that you can apply for the 60-day extension based on Thai family? Example: my exit stamp is April 13, can I just go apply for the extension ASAP to just get this taken care of or do I need to wait until closer towards April 13? And if I am able to go ASAP, I’d still get 60 days added on to that April 13th date, correct? And not the date I apply for the extension?