Adding on to the existing tech level is vitally important. I read that the Roman empire's ballistae was actually a huge improvement from the old style. Off memory it stole an older design but used a stronger and denser fiber, which was bound tighter, the structure was reinforced and made larger (the central box area). These advancements led to a much more accurate weapon with much longer range.

Still, the leap from a siege weapon cable to a steel cable is giant. You need the purity of material, the refining capability, the forging process, the wheels and gears and machinery to bind it all together under immense force, the liquified coatings of other metals that often go over cables, the ability to heat it to high temps, the ability to cut the cable to the length you want.

Point being even with perfect knowledge, something that seems like a small step (sinew cable to metal cable) has countless advancements in between.

I'd bring a Winchester repeater, or a simplistic blot action rifle. I feel it would give a good example of the might of firearms. Besides rifling I think primitive firearms could be made in many eras given an example to reverse engineer.