Final answer:
The increase in our ancestors' brain size did not occur immediately after the adaptation to bipedalism, making the statement false. It took several million years for the significant growth in brain size to happen.
Step-by-step explanation:
The statement that once our ancestors began walking on two legs, big brains followed quickly is false. The evolutionary transition to bipedalism began with australopithecines, and early Homo species like Homo erectus were efficient bipeds, but still had relatively small brains. It took millions of years for humans to evolve from their ape-like ancestors, with a significant increase in brain size occurring only between 800,000 and 100,000 years ago.
H. floresiensis and Homo naledi demonstrated that even with adaptations to bipedalism, brain size did not necessarily increase in lockstep. Cultural and technological developments, supported by larger, more complex brains, were instrumental in human evolution and adaptation to diverse environments, and were concurrent with these anatomical changes.