The first time leaving a plug out can definitely make your heart race. Once you realize because of all the floatation the Coast Guard requires being installed, your boat will likely never sink, even if you leave the plug out indefinitely; you’ll be able to relax a bit.
If your motor is strong enough you should be able to kick it up on plane and the water will drain pretty fast, then if you can reach it put the plug in from the inside. Or stop and put the plug in from the transom if you can reach.
The first time I left it out I docked the boat and walked away for a couple hours. Came back with water over the floor. Hopped in, popped the plug in, turned the bilge on and let it run. Been in the middle of the lake and did the same thing.
It’s more embarrassing than anything.