Apple - Bring all windows of active application to top

You can assign a keyboard shortcut to the "Bring All to Front" menu item from System Preferences:

The activate AppleScript command also raises all windows:

activate application (path to frontmost application as text)

If you are assigning keyboard shortcuts to opening applications, you can use scripts like this:

tell application "TextEdit"
    reopen
    activate
end tell

reopen opens a new default window if there are no open "default" windows, like a text editor window in TextEdit. If all default windows are minimized, reopen unminimizes one of them.

It is also possible to use AppleScript to click the "Bring All to Front" menu item:

tell application "System Events" to tell (process 1 where frontmost is true)
    click menu item "Bring All to Front" of menu 1 of menu bar item "Window" of menu bar 1
end tell