Yes I agree - if something has no beginning then it is uncreated. If something has not been created then I don't understand how it can exist.
I agree that the ideas, the options you present are incomprehensible (to me). I'm not sure that makes them illogical though. But then what is logic? Is it human comprehensibility? Is logic a human construct?
In any case, one of your three options must have occurred, since here we are. I prefer the "it came from something else" line because "something else" is not defined and therefore cannot be expected to be necessarily comprehensible to human minds.