No, NASA also didn't think it was possible at the time. There's an informative little paper here. [1] It only gets more informative from the first sentence, "Mathematical risk analysis was used in Apollo, but it gave unacceptably pessimistic results
and was discontinued." By the time of the launch to the Moon NASA's internal estimates were looking at around a 50% chance of success based on Gene Krantz's (mission controller) "Failure is Not an Option" book.
It was a mission they dedicated themselves to, and humans have this way of making things happen when we actually set our minds to tasks. A reality that's often been lost in modern times as we have mostly moved away from pursuing, let alone achieving, great things in the real world. One of the many reasons to get humans on Mars.
You’re confusing specific low odds of success for “didn't think it was possible.”
The Apollo missions got unbelievably lucky in that none catastrophically failed despite multiple close calls. However, if you’re willing to try multiple times the odds any mission being successful is much better than every mission being successful.
IE: Six missions landed on the moon. If they each had independent 50% odds then six heads is a long way from impossible ~1.6%, but at least 1 head is quite likely ~98.4%. I doubt we would have tried for a 6th mission after 5 failures in a row, but the point is definitions of success matter a great deal here.
Similarly failures improve odds of success in the future because you learn from mistakes and success means the system is functional eliminating some risks.
What I'm demonstrating is that we indeed knew basically nothing. There was no secret tech or expectation of success. Mathematical models doomed the entire idea to failure, and all the way up to the day of the launch people who spent years in a bubble of optimism still didn't really expect more than a 50% chance of success.
On that specific launch, which is another way of saying they believed the project had a very good chance of having someone walking on the moon. Failure there wouldn’t even mean people died, just that they didn’t walk on the moon and then safely get back on that mission.
The exact opposite position after 6 failures would be that the odds were good that at least 1 mission would have succeeded.
Obviously, things aren’t actually completely independent, but 6 lunar landings could have successfully been completed with a huge range of different odds. 50% odds of success on the first launch isn’t inconsistent with 6 successful launches or 6 failures, it’s just not enough data to really narrow things down.
It was a mission they dedicated themselves to, and humans have this way of making things happen when we actually set our minds to tasks. A reality that's often been lost in modern times as we have mostly moved away from pursuing, let alone achieving, great things in the real world. One of the many reasons to get humans on Mars.
[1] - https://ntrs.nasa.gov/api/citations/20190002249/downloads/20...