I have played an infiltrator with a single-shot sniper rifle on silver and gold, and it can work fine, with the right gun and class. The best class options are probably Geth and Salarian, though it is worth considering Human if you don't have the others. I am ignoring semi-auto snipers and shotguns, because I don't use them with infiltrators. They may work fine, but I can't comment on them.
For all three, my weapon of choice is a Widow with thermal clip capacity and damage mods. You can add a sidearm/shotgun if you wish, though I find that I don't miss it too much. You won't be great at close quarters, but your single sniper shot (if you can land it) and melee means you can deal some damage at short range, and you can always cloak and run away if it gets too hot.
The basic infiltrator. You are like the geth infiltrator without hunter mode. You want fitness (max out health/shields), your class power (I maxed out carrying capacity, though you can make a case for weapon damage as well), and tactical cloak (max out damage/sniper damage). You can put your remaining points where you like, but you won't get much use out of them -- cryo blast doesn't help that much, and your sniper rifle should massively outdamage sticky grenades.
On Silver, a cloaked body shot with a decent Widow should one-shot standard infantry (cannibals, geth troopers, assault troopers), and a cloaked headshot should one-shot elite infantry (marauders, rocket troopers, hunters, centurions, engineers, nemesis, phantoms). Depending on your precise weapon/mod/skill choices, some may be left with a sliver of health left, but with the right choices, it is certainly possible to one-shot these sort of enemies.
On Gold, it will take two shots to kill any shielded enemy, so you probably want to find a different class to play.
On any difficulty, you will demolish heavy enemies - a widow 1 shot deals ~850*2(general damage bonus+cloak damage bonus)*1.4(cloak sniper bonus)*2.5(headshot)=well over 2000 damage without a headshot and almost 6000 damage if you can get a headshot -- about the only thing that can possibly compare to this is biotic combos and missile launchers.
Put points similar to the Human Infiltrator, except that the remaining points go into Hunter Mode. You basically end up with the fewer hp, all the important skills from Human Infiltrator, and Hunter Mode. This is a very good trade. As side benefits, Hunter Mode gives you increases to damage, movement speed, power recharge, and other assorted areas. All of these things are useful. The biggest thing, however, is the vision. You can now see invisible enemies, see through walls, and see through cover. Knowing exactly where everything is is priceless -- particularly combined with your movement speed, you can outmaneuver everything else on the map. It's also fun getting headshots on invisible hunters. In short, the Geth Infiltrator is the human infiltrator, but better.
In practice, both infiltrators will play similarly. You will have a slightly easier time one-shotting things on Silver (because of the damage bonus), but you will have an equally difficult time on Gold. I highly recommend the Geth Infiltrator on Silver, but you can't kill shielded enemies fast enough on Gold.
Again, you get fitness, your class power, and tactical cloak (take sniper damage, not bonus power -- trust me). However, you also get Energy Drain (ignore proximity mine). This is your life saver on Gold. There are a couple of things to note when not taking bonus power:
- If you break cloak with an energy drain, the recharge time is the recharge time for cloak, not energy drain (if you were only cloaked briefly, this means that the recharge time is fast).
- When you break cloak, the damage bonus sticks around for about 2 seconds (this means that if you break cloak with an energy drain, you have enough time to get a sniper shot off that benefits from the cloak bonus damage)
- Energy drain (and other powers) benefit from the cloak damage bonus.
- Energy drain often knocks back/stuns the target, making your follow-up sniper shot easier to land.
Put together, this means that you can cloak, use energy drain, and shoot with your sniper rifle, and then wait for reload/power recharge. The energy drain will punch through most shields in one shot (phantoms, hunters, and pyros will take two energy drains, but other infantry will generally only take one), the follow up sniper shot will one-shot the now-unshielded enemy, even with a body shot. This works reasonably reliably, even on Gold (its my favorite class/build on Gold). Energy drain also gives some free bonus damage against larger targets and replenishes shields, as well.