What we've tried so far, after extensive googling and keyboard-only navigation as suggested below: Hoping someone can suggest a keyboard-only fix that we haven't tried. Most solutions online don't exactly match this issue, or suggest fixes that require the use of a cursor, so we're a bit stuck.
The laptop does not have a touch screen, so we have no way of interacting with things normally.
They usually use a wired USB mouse, but the trackpad is doing nothing as well. It's present at the login screen, and gone immediately after.
A family member has a laptop with Windows 10, and the cursor has completely vanished.