In Lightning Web Components (LWC), the lifecycle hook that is called after the component is connected to the DOM is the connectedCallback.

connectedCallback:

The connectedCallback lifecycle hook is executed when a component is inserted into the DOM (Document Object Model).

It's useful for performing actions that should happen once the component is connected to the document, such as fetching data, initializing variables, or setting up event listeners.

This hook is called after the component's template has been added to the DOM.

Example:

In this example, when an instance of ExampleComponent is inserted into the DOM, the connectedCallback is triggered, and the message "Component connected to the DOM" will be logged to the console.