Not true. Climbing trees for millions of years taught us nothing about orbits, or rockets, or literally incomprehensible to human distances, or the vacuum of space, or any possible way to get higher than a tree.

We eventually moved on to lighter than air flight, which once again did not teach us any of those things and also was a dead end from the "get to the sky/moon" perspective, so then we invented heavier than air flight, which once again could not teach us about orbits, rockets, distances, or the vacuum of space.

What got us to the moon was rigorous analysis of reality with math to discover Newton's laws of motion, from which you can derive rockets, orbits, the insane scale of space, etc. No amount of further progress in planes, airships, kites, birds, anything on earth would ever have taught us the techniques to get to the moon. We had to analyze the form and nature of reality itself and derive an internally consistent model of that physical reality in order to understand anything about doing space.