Natively in ST, it requires hosting a SmartApp that can receive events and issue the webhook. There are some Edge drivers that can be run on a ST hub that can send HTTP/S requests and be used in ST Routines, but ST hubs can only talk to private IP address space so you have to run a proxy to reach outside of your local LAN. There is a discussion in this topic about options.
Can’t speak to whether there is an API you can call to initiate Alexa routines or not.