Is there a way to get the moment the current page is displayed

For example, in the figure above, I want to get the date that the box is framed on

There is no built-in way to get the viewport dates. But you can use the Gantt API for that.
To get the left position, you need to use the getScrollState method:

To get the right position, you need to add the width of the gantt.$task element to the scroll position.

Then you need to convert the position to the date using the dateFromPos method:

You can see how it works in the following snippet: