"All the evidence seems to indicate, that the universe has not existed forever, but that it had a beginning, about 15 billion years ago. This is probably the most remarkable discovery of modern cosmology."
Yep, that's exactly what that specific quote out of a lecture from says. I've read that lecture many times. It doesn't say what your claims are. It's very easy to take an old quote out of context and make incorrect claims about it. It's much harder to stay up to date and understand nuance.
Sorry. Words are hard. Here's another quote for you...
Quantum theory introduces a new idea, that of imaginary time. Imaginary time may sound like science fiction, and it has been brought into Doctor Who [an English Star Trek]. But never the less, it is a genuine scientific concept. One can picture it in the following way. One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there's another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time.
And another...
The beginning of real time, would have been a singularity, at which the laws of physics would have broken down. Nevertheless, the way the universe began, would have been determined by the laws of physics, if the universe satisfied the no boundary condition. This says that in the imaginary time direction, spacetime is finite in extent, but doesn't have any boundary or edge.
And another...
The no boundary proposal, predicts that the universe would start at a single point, like the north pole of the Earth. But this point wouldn't be a singularity, like the Big Bang. Instead, it would be an ordinary point of space and time, like the north pole is an ordinary point on the Earth, or so I'm told. I have not been there myself.
