Keyboard shortcut for moving cursor to top of page?

Is there a keyboard shortcut to move the cursor to the top item of an outline?

You can paste the following omni-automation code in the console:

(() => {
    const
        e = document.editors[0]
    return e.select([e.rootNode.children[0]])
})();

Is this is what you want, could be possible to improve it. The script above selects the top-most descendant of the outline (assumes there is at least one).

You can set the keyboard shortcuts for most actions. There is a menu item:

OmniOutliner > Keyboard Shortcuts…

Within it, there is a ‘beginning of document’ and ‘end of document’ but they don’t seem to do anything for me.

Consider contacting Omni support to enquire. You can create an email using Contact Omni from the Help menu.