''Surely it can't just self-generate such properties via good fortune?''
Well, that is the essential problem. Nobody actually knows why the properties of matter/energy have the values they have, rather than something else.
So the correct position is - ''we do not know''
The incorrect position is....''well, it must be the work of a Creator.''
There is nothing to say there must be a creator. There are other possibilities, perhaps something not yet imagined. A creator is not the only option on the table.
Whatever the case may be, the fact remains that nobody knows.