Magento 2: Initialize Ui Component after page load

I have a module with a Ui Component that is part of a magento widget (based on the Magento chooser widget). At one point, the widget makes an AJAX call that pulls in a view (a .phtml file), which is where I want to initialize the Ui Component.

However, if I try to initialize the Ui component via JSON, i.e.:

Magento does not initialize the Ui Component or bind it to the dom elements. Is there a way to “manually” trigger the initialization and binding of the Ui Component?