The picture book market can be a challenging one to break into as a new author or illustrator. However, there are publishers that accept submissions from unagented creators. Some tips for submitting your work to publishers include:
Researching the publisher to make sure that your work aligns with their interests and guidelines.
Following the submission guidelines carefully, including any formatting or file requirements.
Creating a strong cover letter and submitting a polished manuscript or portfolio of illustrations.
Being prepared for rejection and continuing to submit your work to other publishers.
It's also worth noting that some publishers may not accept unsolicited submissions, and may only work with agents. In this case, you will need to find an agent who is interested in representing your work.
Finally, joining a writing group or taking a course in children's book writing can help you to improve your craft, and to connect with other authors and industry professionals.