If i remember correctly the spartans were already trained and they took out Colonel Watts and then the covenant took out harvest so the spartans were rushed to Chi ceti as soon as they heard so that took like 6 months-1 year at the most so that leaves 4 years to go help retake harvest then we are at the setting of the game
If i am wrong just tell me i am not infallible and i haven't read the books for a month and i haven't got the game YET so i am going on memory and best guess
Even the greatest warrior quails in fear at my name