While Opera is fully close and there are no Opera processes in the Windows task manager, you can delete the "Sessions" folder in the profile folder. Path to the profile folder is shown at the URL opera://about. Just note that will wipe out all your tabs too.
While Opera is closed, you can edit the "Preferences" file in the profile folder with JSONedit in tree mode. Under root/browser, you can right-click on the "window_placement" node, choose "Delete selected node" and then save your changes. That will put things back to default.
You can also right-click Opera's desktop shortcut, goto "Properties", switch to the "Shortcut" tab and examine the target field's value to make sure there are no command-line switches being passed to opera.exe to tell it to start minimized. For Opera's taskbar button, you can do the same by right-clicking it and then right-clicking "Opera Browser". Also on the "Shortcut" tab for those, you can check the "run" setting to make sure it's not set to "minimize".
Besides all that, it might be one of your extensions at the URL opera://extensions.