You will not break his sustain. Just focus on farming only. Once you hit 6 you will be able to out trade him however, and out damage the heal from consume as well assuming you've been farming properly.
The last Nunu I played top as Jax had roughly twice my CS until I hit 6. After that I killed him three times (once with jungler intervention, once by flashing out of his ultimate right before he activated the burst, and once by igniting him right before he consumed a minion after a fight).
Always carry a ward to leap strike to as well, but this applies to any matchup as jax.