It really is that fast. And you have to stay on top of the lock situation. Mine didn't have the dexterity to turn a deadbolt until suddenly they did one day, when I stepped into the kitchen to pour a cup of coffee. Older sibling, thank god, yelled out "no!" Even with immediate notice that child had run out the door, I still had to haul ass down the street barefoot. Their speed is incredible when the impulse to run takes over.
The backpack leashes are lifesavers. We used one for years, and have only recently gotten rid of it because kiddo is too sick to run as fast as they used to.
And yes, I've slept in front of doors too.
Whatever locks you have now, start looking for the next step up. Chain locks at the top of your reach, audible alarms on external doors & windows, depending on the style of window you have in your house there are several types that will allow for like a 1" opening for air circulation without letting it open enough for a kid to get out. We never had to go this route but some parents do need to put bars on windows. Make yourself aware now of the options available so you're not scrambling for a solution if things progress down the line.