Thank you for confirming for me that there was not a published API currently.
We are deploying single page applications, dependent upon the Okta Sign-in Widget, to numerous environments (e.g. staging vs production). These environments are accessible from unique hosts via our proxy. When initially deploying to these environments an update to the Trusted Origins configuration is necessary.
We are also investing heavily in a containerized infrastructure and progressive delivery process. With this endeavor we are automating everything we can. We would like to automate the configuration of the Trusted Origins as environments are constructed dynamically at times (primarily to support automated integration testing).