I have never been to ancient Greece, because I am not capable of time travel...but I've written about ancient Greece. With enough research, authors have the ability to write about pretty much anything -- any environment, any setting, any action. But if you want your book to feel real and resonate with readers, use your experience. Personal experience can be translated to any character in any setting...if you know how.
In My Shoes
A strong literary character is only strong because of what happens to them in the book. Suffering loss, getting married, being heartbroken, going hungry -- these things make a book interesting and can shape a character throughout its pages. If you haven't experienced these things, you can still write about them. But if you choose to write about things that have happened to you instead, your book is going to be much richer.
You've been hungry before. You probably know what it's like to feel pains in your stomach, to feel the lethargy of an empty belly and the sharp awareness that comes with deprivation. And if you haven't felt that, you may not want to include a starving scene in your book (because how would you know?).
But maybe you have been full. Perhaps you've swam in the ocean, or been inside a fitting room with lots of clothes to try. Even the small, mundane experiences you've had can be used to create a rich tapestry for your book. If a killer is stalking your heroine, why not put her in a tiny fitting room and have the stalker show up in that situation? You've been inside the room before, so you can no doubt imagine all the rest. If you've been to an amusement park, send your ensemble cast of characters off on an adventure of their own.
Use your experience to paint more realistic pictures, good stuff and bad stuff. Boring stuff and amazing stuff. Weave those real experiences into your fiction, and it will come together to create a journey that feels more lifelike to your readers. Good writers can turn eating eggs into a thrilling action scene. So sit down, have some eggs, and turn that into literary gold. I know you can do it.