Certainly not impossible but HIGHLY unlikely.
Let make a suggestion that may save you a lot of money.
Setting unlikely goals often leads to failure. I am not quite sure of what your motivation is to go for a >4 Sharpe ratio. Is it to be noticed on ET, is it to inflate your ego, is it to become rich?
I don't expect a response to these personal questions.
Why not set a goal of maintaining a Sharpe ratio >1 this will already put you ahead of the majority (vast majority).
Setting unreasonable goals and then trying to chase them is a sure recipe for disaster.
Good luck. I would be happy to be proved wrong but think about the probabilities.
Mike