The pedal "feels" better with the engine off as there is no power assist, making the pedal hard to push. Starting the engine make the booster multiply force,revealing then ...that you have no brake pressure.
A few things here...
Is it a disc /drum setup?
Disc /Disc ?
Anytime a master cylinder is mounted low on the frame, residual pressure valves need to be installed .
A residual pressure valve holds the wheel cylinders/ pistons in calipers closer to the friction area of the drum/rotor. Taking up any slack, making the pedal travel required to activate the brakes considerably less.
Another thing to consider is the bore size of the master cylinder, if the bore is too small, it wont be sufficient to move the disc brake pistons out to begin with.
More info on your system is needed.
Fact is stranger than Fiction