A Branch Site can be converted to a Core Site when:

In Genesys Cloud CX, a Branch Site can be converted to a Core Site when an Edge is assigned to the Branch Site. The Edge device is essential for routing and managing interactions, and its presence elevates the site from a Branch Site to a Core Site, giving it the full capabilities associated with Core Sites. This conversion is part of the network architecture and is critical for managing and optimizing interaction routing and resource allocation.

References:

Genesys Cloud CX Site and Edge Management Documentation​​​.