To distinguish between new and returning customer you need to configure the pixel events through Google Tag Manager GTM.
To configure the Facebook pixel and conversion API through Google Tag Manager you would need a custom datalayer where we can get custom data based on cookies and session data.
When we have customer data, we can send different purchase event to facebook pixel with the help of datalayer and Google Tag Manager using datalayer variable.
Here I have attached an image where i configured datalayer for one of my clients with new customer data true or false.