I don’t ascribe to this meaning of the word eternal. It certainly doesn’t apply when the Bible speaks of eternal life either. The word in greek is αἰώνιον and it means everlasting, so having no beginning has nothing to do with it. And anyway, I don’t believe hell is a creation of God and I certainly don’t believe in a hell which always existed. The hell I believe in is something people create – like we see it in the world.
The plain fact is that at the end of Matthew 25, Jesus says…
"And they will go away into eternal punishment, but the righteous into eternal life.”
And I don’t see how babbling about there being no hell which “never did begin and never can end” changes that in the slightest. You might as well argue that there is no eternal life because our life had a beginning.