Is it possible to expand toolbars by default in ArcGIS Online Map Viewer?

Answer

No, it is not possible to expand the toolbars by default. However, when the Map Viewer toolbars are expanded in the browser, they are stored in the browser cache. Therefore, the toolbars remain expanded when revisiting Map Viewer.

Alternatively, use the keyboard shortcuts to perform actions on the application, layers, and map view in Map Viewer. To view the list of keyboard shortcuts, click Information on the toolbar. In the Information window, under the Shortcuts section, click shortcuts.

Note:
The full list of keyboard shortcuts can also be viewed by pressing Alt+? on Microsoft Windows or Option+? on Mac. 

The image below shows the list of keyboard shortcuts in the Keyboard shortcuts window to complete common workflows in Map Viewer.