You know, I admire subtlty. For instance, I admire the subtle way in which your question is phrased, specifically the part about, “‘An’ Evolutionary Theory explanation.” You got me! I suppose there could be out there, somewhere, perhaps in the most obscure filing cabinet in a dark corner of the basement of the Discovery Institute, "an" evolutionary theory explaining how the origin of the first living cell is part of the TOE. But that particular, rather eccentric version of the theory hasn't been peer reviewed, like every other accepted scientific theory has been, so it really doesn't matter much.
Or, at least it hasn't to my knowledge. If I'm incorrect on this, please let me know and I'll be happy to retract that statement.
What I do know is this: “inanimate matter evolving into the first living cell” is outside the current TOE. I know this because I've read the theory and understand it, to some limited degree. I do not feel qualified, however, to insist that the theory is flawed or wrong if it fails to address some personal hobby-horse.
That's incorrect. You don't know it; you are surmising it. You'd have to know the mechanism by which inanimate matter evolved into the first living cell to actually know it.