I don’t believe it could.
For the universe to be uncaused, it must, as the quote suggests, be eternal. But we can easily show that the universe cannot be eternal, because the very suggestion leads immediately to a logical absurdity: if the universe were eternal, then the past would be infinite. If the past were infinite, we would have to traverse an infinite amount of time to arrive at the present, and as there is no end to infinity, we would never make it to this moment.
Ergo, the universe began to exist. Ergo, the universe was caused.
Much more could and has been said on the subject.