You don't mean at boot, you mean at desktop session startup (which you may have configured to happen automatically when you boot).
Opera can be started via the desktop's autostart facility, either directly or via a wrapper program such as a shell script if you need more features than the plain autostart gives.
AFAIK there is no way to tell opera to start up minimised, neither by command line option nor by the many configuration options detailed here
That leaves the possibility of having your desktop's window manager (Ubuntu, so Gnome desktop, so metacity window manager?) make opera start minimised. If it is metacity then you may be out of luck because it is (by design) one of the least configurable window managers.
If the window manager cannot be used directly then it may be possible to use a window launcher utility such as wmctl (or wmctrl?). I am not yet familiar with them but they may be able to both start opera and tell the window manager what to do with its window. In this case a wrapper program may be necessary.