Could an airliner exceed Mach 1 in a zero-G power dive and safely recover?
There is actually some data (albeit limited) on this scenario:
On August 21st 1961 this test was performed in a DC-8. When this test was performed they were supersonic for about 16 seconds which took a lot of planning to pull off. You first need to climb higher than the plane typically does to have enough altitude to pull this off, then make sure you understand how the control surfaces are loaded in the dive. You get out in once piece by planning for it and understanding exactly what's going on:

We took it up to 10 miles up, 52,000 feet—that’s a record—and put it
in a half-a-G pushover. Bill maintained about 50 pounds of push. He
didn’t trim it for the dive so that it would want to pull out by
itself. In the dive, at about 45,000 feet, it went to Mach 1.01 for
maybe 16 seconds, then he recovered. But the recovery was a little
scary. When he pulled back, the elevator was ineffective; it didn’t do
anything, so he said, “Well, I’ll use the stabilizer,” and the
stabilizer wouldn’t run. It stalled, because of the load. What he did,
because he was smart, is something that no other pilot would do: He
pushed over into the dive more, which relieved the load on the
stabilizer. He was able to run the [stabilizer] motor, with the
relieved load, and he recovered at about 35,000 feet.

Remember you're diving fast, really fast, so you likely can't go much faster as you will ultimately run out of time to accelerate:

The Mach number itself isn’t used in a dive as a target because it’s
much more accurate to use airspeed. So every thousand feet I would
read off to Bill the airspeed [he needed] at the next altitude. As we
were coming down, I was talking almost all the time because at a
descent rate of 500 feet per second, every two seconds we were 1,000
feet lower. Looking out the window—which I stopped doing—it looked
like it was straight down.

The trick is to not over stress the airframe.