I'm no supporter of the imaginary group, CANOE...the Campaign to Ascribe Nautical Origins to Everything...but I actually do believe this phrase may well have originated as sailors' slang.
In Smyth's Sailors' Word-book, published in the 1850s, the phrase 'to crack on' meant 'to carry all available sails'. Perhaps there was a connection with the whipping sound sails often make in the wind.
There is no record of 'get cracking', as such, before the 1930s, but - given the idea of 'speeding ahead' - I wouldn't be surprised if there was a connection.