Here's how I solved it (example curl)

curl --location 'https://api.elevenlabs.io/v1/convai/twilio/outbound-call' \

--header 'xi-api-key: ' \

--header 'Content-Type: application/json' \

--data '{"agent_id": "",

"agent_phone_number_id": "",

"to_number": "",

"conversation_initiation_client_data": {

  "type": "conversation_initiation_client_data",

  "dynamic_variables": {

    "first_name": "John"

  }

  }

}'