Do we know whether the moon has been tidally locked since the time of its creation

Yes, we do know! And the answer is that there once was a time when the moon was not tidally locked to the earth! We know because the USSR, then the US, then China went there and were able to take very fine magnetic readings on the moon which show that at one time there was a magnetic field on the moon. We now know that magnetic fields require a spin in the body, a solid(ish) core and a liquid mantle. Mars has the spin, but no liquid mantle. Venus has the solid core and liquid mantle, but not the spin. So the US and the USSR placed moonquake monitoring gear on the moon in the 60's and 70's, and with that data were able to get a very good picture of the internal structure of the moon. They were also able to see that rocks on the surface are magnetized, and those rocks show a pattern of a field that required a faster rotation than we see today.

We also know that the moon was closer to the earth in the past, and that over time the earth and moon have been trading energy back and forth via gravity (this is not 100% correct but the analogy fits stick with me). The days on earth have been getting longer, the moon has been pulling away (and still is about about an inch per year) and eventually, the earth's rotation will slow so that the earth and moon rotate at the same speed and are tidally locked with each other. (There is some debate on if this will happen before the sun consumes the earth in a few billion years or not, or if the earth will be able to hold onto the moon at that point.)

And here is why I love science and curiosity. We know that the earth's day was roughly 21 hours when the dinosaurs were living due to fossils and math. This article from six years ago is also a good primer on the HOW we know that these things are facts and how they explain what we see on the earth and on the moon today.

Procellarum was probably an impact, but it can also be explained with frictional heating, the offset core of the moon and mantle plumes. Imbrium is definitely an impact crater.

The only way to solve this mystery is to go back, collect rocks, build a base and begin to explore the moon in depth.