If Salesforce is a new addition to the overall application layer and you cannot use Salesforce's routing engine, external routing allows work items to be routed based on an external application, which will decide which agents have enough capacity and the skills to handle a work item.
To find out more about this routing model, and if you feel you want to join the developer side of things, please refer to the Omni-Channel developer guide at https://developer.salesforce.com/docs/atlas.en-us.218.0.omni_channel_dev.meta/omni_channel_dev/omnichannel_developer_guide_intro.htm.