How do I use the green square/fill handle without a mouse?

How do I double-click Excel's green fill handle without using a mouse?

In Excel, when I select a cell, there is a small green square (fill handle) at the bottom-right corner. If I double-click that green square, Excel automatically fills the formula/data down the adjacent column.

Is there any keyboard shortcut or keyboard-only method to perform the same action as double-clicking the fill handle?

I don't want to drag it—I specifically want the double-click AutoFill function without using a mouse.