It seems that few people on the Internet have any knowledge of accessibility because any search for this issue brings only up the ⇧ Shift +right-click trick. For numerous reasons, it is not always possible to use the keyboard and mouse at the same time. Here is how you can accomplish it with just the mouse and just the keyboard:

With only the mouse, right-click one of the taskbar buttons, left-click a button, wait for the Aero Preview window to pop up over the button, right-click it to open the context-menu, then click somewhere else to dismiss the menu.

With just the keyboard, hold the ⊞ Win key and press a number corresponding to one of the taskbar buttons—e.g., ⊞ Win + 1 to access the first button. (Alternately, you can press ⊞ Win + T to focus the taskbar, then Tab to the first button.) Now you can press the ▤ Apps/Context key to open the context-menu, then Esc to dismiss it.