"From the get-go" does not appear in print until the 1960s, apparently. Some think it morphed from the expression, "From the word 'go'"; personally, I think the similarity is coincidental (due to the opposing rhythmical stresses in the two expressions; 'the GET-go' would not naturally emerge from 'the word GO').

Another theory is that it is an abbreviated version of "Get ready, get set - GO!"

Yet another theory has it as coming from the clunky formation "getting going" - I think "get going" more likely.