I sat in on a webinar conducted by Mira Reisberg of the Picture Book Academy and Miranda Paul of Rate Your Story. The webinar, which was called “Ten Things You Must Know Before Submitting your Manuscript”, was fabulous.
One tip that Miranda gave was that although a publisher says it is closed to unsolicited submissions, you can send a query letter to find out if they will accept your manuscript. So in other words, although they will not welcome unsolicited manuscripts, if you query them first, and they like your idea, you have now opened a door by making your manuscript solicited.
Just make sure that you do your research first and that your manuscript is a right fit for the publisher.