Blocked all edit triggers by setting editTriggers to NoEditTriggers.
Implemented editorEvent() in the delegate to recognize a mouse press and calling edit() manually.
In the created widget I implemented showEvent(). In it I check if it's the first show event or not. If it's the first I synthesize a fake mouse release event followed by a mouse press event and send them to the app via QApplication::sendEvent(). Some attention was needed to make sure the fake events are with the same mouse buttons and other event options, otherwise you can easily confuse the internals of the view.

This way Qt does all the work to figure out which widget should get the focus and mouse press, how to route it through the item view etc. You can probably extend this to other trigger methods. You would just need to tell the widget somehow about which trigger method was used and act accordingly in the showEvent() e.g. set focus on the "first" widget when it's via tab key and so forth.

One possibility could be to use QApplication::widgetAt in your editor showEvent and check there which widget is under the cursor to give it the focus.

The QTreeView::mousePressEvent()
triggers QStyledItemDelegate::createEditor(); and QStyledItemDelegate::setEditorData();.
However, now the click needs to kind of be repeated on the created editor Widget.