Can you use a machine to gain both force and speed at the same time

 It rather depends on your definition of "machine". The normal physics set of simple machines - levers, pulleys, ramps all give you increased force at the expense of reduced speed or increased speed at the expense of reduced force. 
So, no - by definition a machine is an arrangement for multiplying one while paying the cost by reducing the other. You are looking at an example of the Conservation of Energy... one of the giant rules we are pretty sure cannot be violated.