Well... Kind of.
You don't really grow out of it, so much as you learn to adjust to the world around you.
Okay, let's use a physical example that might be a little more intuitive. Say you're born with some kind of dwarfism. Your adult height is predicted to be around 3-4 feet tall, so you're a great deal shorter than everybody your age, and you always will be.
You have problems reaching things. Everything's too big for you. You just don't fit into a world where everybody is nearly twice as tall as you are. However, as you grow older, you learn things that help you, with your small height, adjust to all those things that were made for bigger people. Maybe you carry a step stool. Maybe you get hand controls for your car. Maybe you buy or make smaller furniture for your room. By the time you're an adult, you know all the tricks of the trade, and you can make your way through life no-problem despite the size mismatch.
Autism is a little bit like that. You're born with autism; you're not born with the skills needed to live in a non-autistic world. Ideally, as you grow, you get therapy, education, and you probably teach yourself a lot of skills too. By the time you're grown, it's possible not to need any help anymore even though you've got an autistic brain like you always did--just like the little person who doesn't need any help even though they're still short.
When that happens, when a person learns enough that they don't need help and don't use a lot of extra effort, we often say they've grown out of autism. What they've done, though, is more like growing into a person who can navigate the non-autistic world.