It’s a mistake to think this means “we don’t use freelance contributions”.
It means “we don’t read articles you send us that we’ve not asked you to send us”.
If they really want to try to put you off, they’ll say something like “Unsolicited articles are not read and cannot be returned” and perhaps add “no liability for materials submitted can be assumed”.
These are basically light deterrants to put less dogged or experienced writers off. Don’t be defeatist. 99% of publications accept freelance work.
How to overcome the obvious hurdle, then? Logically, if unsolicited articles are not accepted, one can confidently assume that solicited ones are.
Your task, then, is to get them to solicit an article.
How do you get them to do that? You propose one. You send them an outline – often called a pitch. 100 or 150 focused, compelling and confident words, outlining your idea and designed to be totally irresistable to an editor starved of scintillating material for his or her publication.
They may say, “No thanks”. That’s fine: re-angle and/or rework it and take it elsewhere.
They may ask you to submit the piece on a speculative basis. That’s a solicited article, so write it and send it off.
They may commission the piece. That’s most definitely a solicited article. Congratulations, you’ve just made a sale.
Found this Mistake useful? You might also like my ebook 50 Mistakes Beginner Writers Make (Kindle edition), priced £1.99 / $2.99.