A single Purkinje cell may have tens of thousands of such inputs. Some are excitatory, others inhibitory, and the possible combinations on a given Purkinje cell are in the trillions. Multiply that by the tens of thousands of Purkinje cells, and you can readily see that the possibilities of integrating input and output are nearly infinite. The final output of any given Purkinje cell is via a single axon, but all the Purkinje cells are doing this simultaneously, taking sensory information from all parts of the body and sending output to the appropriate parts of the CNS that controls the effectors. This colossal parallel processing capability allows a falling cat to carry out almost instantaneously the numerous decisions about postural control, muscle tensions, etc. before hitting the floor.
Breathing is truly automatic and a newborn baby can breathe properly.
The time to do this varies considerably among species. The helplessness of kittens and puppies, who require weeks to learn to walk and run, is due to the fact that in those animals the development of the cerebellum is not complete until a few weeks after birth. In humans the process takes longer. If the cerebellum doesn't develop fully, an animal may never develop proper coordination. A variety of causes may result in cerebellar hypoplasia , an underdeveloped cerebellum being the result.