Rules-wise:
Firstly, the PCs - Are they aiming as an action (+10% to hit)? Are they using weapons with decent ranges? Are they not wanting to get into close combat (if they're better at close combat)?
Secondly, the enemies/NPCs - have you considered moving them in closer? Tried to make flanking manoeuvres that expose them? Typical tactics for most fighting forces are to not sit in one place but to try and get an advantage on the enemy through moving around to find a weakness. You're in control; if the PC can't hit them as part of a "demo" session then control the enemies to get them closer so the PC can hit them.
Thirdly: have you got enough dice? Getting enough dice to cover the various rolls to roll in one go can usually speed up the process, bar the occasional bonus damage rolls which can occasionally happen; dice rolling can at times make the fights feel slow.
Finally, its a 1-on-1 session; a single low-level character won't be much good on their own, particularly against a large group; there'll be a better sense of enjoyment when you have more PCs involved.
Fluffwise:
Some of the suspense and excitement can come from the descriptions you give; a missed shot can be "chunks of plascrete shatter off from the top of the wall you've fired at, ricocheting wildly" or "a roiling ball of plasma erupts near where you crouch, immolating an unlucky Milliasaur as it moved across the now scorched wall across from you".
Its all about how you control the fight given what you have and what the player(s) choose to do.
PS: most low-level characters don't hit much, even with power-building and good dice rolls; suggest players spend experience in their relevant stats, skills or traits when they can - by about 3-4 level they should be more than happy that they can hit things fairly often.
