Hello there! Currently, we don't have external/traditional APIs to call Clay outside of the main UI. One of the reasons we don't have external APIs enabled is because we have several tools that already work under API systems and thus it would be a complex setup given the variety of actions you can implement within Clay, at least for the time being.
It can still work similarly with tools we have like Webhooks to auto-import records into a workflow and then using HTTP API integrations to push it to your custom API.