This is a great question! Three approaches come to mind to invite writers to participate and grow the conversation around your publication.
One is to focus on exploring the topics you're interested in and reading stories in those topics to find writers. You can start building relationships with writers you find by following, reading, and responding. As you build these connections, you can extend the invitation to participate.
The second is to explore ways to make the conversation welcoming and inviting to new writers. What sort of support might they receive?
The third is to leverage audiences you have on other platforms by extending the invitation there as well, for instance through social networks, or through an email list.
I'll make a note of this for a future discussion question, and curious to hear responses from others too!