To create a row post a JSON object whose keys are the names of the columns you would like to create. Missing properties will be set to default values when applicable. 
curl "https://integration.getmateo.com/api/v1/contact" \
 -X POST -H "Content-Type: application/json" \
 -d '{ "full_name": "Max Mustermann" }'

HTTP/1.1 201 Created
No response body will be returned by default but you can add a select query parameter to select the columns that should be returned: 
curl "https://integration.getmateo.com/api/v1/contact?select=full_name,birthday" \
 -X POST -H "Content-Type: application/json" \
 -d '{ "full_name": "Max Mustermann" }'

HTTP/1.1 201 Created

{
  "full_name": "Max Mustermann",
  "birthday": null
}