I don't have to. YOU set the standard at "the existence" of the LXX. Which CAN be established with the DSS.
It appears you are claiming there is such a thing as a Septuagint. There isn't.
Oh... so you ARE denying it existed at all now? Can you cite a single reputable scholar who makes that claim? Tehre are dozens of qorks comparing the NT citations of the LXX vs. the MT but none of them really understood that the LXX never really existed?
Why don't you just tell me how old the earliest available version, or portion of one, is.
Didn't we just go over this? The oldest semi-complete manuscripts of ANY Scripture are the DSS, Though first and second century church fathers refer to them and the oldest codices are obviously based on them.
What's the "oldest available version" of the OT that is NOT the Septuagint?