Is it normal for a first-time author to pay out of pocket to have a book published?

No, no, never. A reputable publisher does not ask an author to pay out of pocket to have a book published. Vanity press publishers do, however. But they will print anything that anyone submits. There is no editorial standard, and that's why people laugh at self-published books and most bookstores won't handle them.

You're not really asking a meaningful question.

Lots of amateur authors pay to have books published. This is called vanity publishing. It has _nothing_ to do with becoming a pro author, any more than me paying to be in my local amateur orchestra is going to lead to me becoming a pro violinist.

People who want to become pros don't pay to have their books published. They submit them to commercial publishers, normally via agents.

There isn't a path whereby you pay to have the first book published and it's so wonderful you are paid for all the rest. Well, there is...sort of. Christopher Paolini managed it. I'll lay money nobody here can name another five authors who did. You're more likely to win the lottery.

Absolutely not. A writers should send their works to respectable publishing houses or magazines. Typically authors must send out hundreds of manuscripts before one is accepted. In the reference section of the library you can find books that tell you where to send your work. Many list names and addresses of Publishing houses. They also tell what particular publishing houses say they accept, & they provide a description of what established authors say they have actually accepted if it is different from what the publishing house claims. They tend to list many other helpful hints for authors too. Most importantly what to include in your cover letter or abstract, yes you need one.

Writers Digest publishes the most popular of these reference books. A Writers Guide to Fiction, A Writers Guide to Poetry & many others. In fact here is the Writers Digests website:

www.writersdigest.com

You can see some of their titles, competitions, & they have a lot of good stuff for writers. Most authors own several writers digest books. You can usually find them all in your local library too.

Good luck, I hope you get published.

If you are self publishing then yes. If not, then it's a scam. If you don't know what self publishing is, then it's most likely a scam.