Ticket System Integrations - PD open a ticket first

Looking for a ticket system integration that will create a ticket for every PagerDuty incident created. We use Live Call Routing (LCR) so we are looking to capture all the after hours calls into a ticketing system. Is anyone else using ticket integration this way?

I see Zendesk is unable to do this (https://support.pagerduty.com/docs/zendesk-integration-guide):
Will PagerDuty create a new Zendesk ticket if there’s a non-Zendesk-generated incident on the same service?

No, PagerDuty will not create a new Zendesk Support Ticket if there’s an incident that did not originate from Zendesk.

Many of our integrations do this by default (ServiceNow, Jira, etc). I see many integration options like Zapier that may be used to receive webhooks from PagerDuty and automatically create a Zendesk ticket for you. You could create the same on your own if you have access to something like an AWS Lambda to receive the PagerDuty webhook and make the HTTP POST to Zendesk creating the ticket.