Automate Sales Order to Invoice and Payment

I am new to ERPnext. I understand the process of Sales Order > Sales Invoice > (Payment Request) > Payment Entry process. But it feels like a monotonous repetitive job.
Say I am selling services(so there is no delivery) through my existing site and collecting payments directly using a Gateway.
How do I get those entries automatically populated into ERPnext?
I tried using the Frappe REST API to create the docs. I am able to create Sales Order. But how do I convert them to Invoice, Automatically Email the invoice to the customers and possibly also record their payment?
I tried
https://<site-base>/api/method/erpnext.selling.doctype.sales_order.make_sales_invoice
but it throws exception
Failed to get method for command erpnext.selling.doctype.sales_order.make_sales_invoice with module 'erpnext.selling.doctype.sales_order' has no attribute 'make_sales_invoice'