Does order matter when drawing player cards? (Efficient to Sequence + Epidemic)
Order does not matter; you draw both cards at the same time. And if either is an Epidemic, you must resolve it first before curing a disease.

From the FAQ


  If we have the 2nd beneficial mutation, exactly when can we discover the cure?
  
  
    You can do it out of turn, but you can’t so it halfway through an epidemic. It’s also worth noting when drawing player cards, you’ll have to discard down to hand size before curing.