Although I'll agree with you that it's rather unrealistic, having lame, talentless starting soldiers is a long-standing gameplay tradition in the UFO/X-COM series. I can't think of a single game where any soldiers you could get started out competent or excellent in any given area. There's no way I know outside of editing your save games to get starting soldiers that are extremely competent in one or more areas.
On the bright side, soldiers improve with combat and experience, so if you can bite the bullet, deal with the lame stats, keep them alive and win your missions, your soldiers will eventually become howling demons of men and women, capable of putting a hole through a Taman's eye at a hundred meters with a snap-shot. Helps to use high-accuracy (low spread) weapons early on and some degree of autofire. Sniper Rifles and Assault Rifles are great primary infantry weapons early on, alongside flamers and grenade launchers for your heavy/explosives. Upgrade to Bolter and Laser weaponry as soon as you can, but keep the flamers and grenade launchers around. Never, ever send a guy out without some form of armor on. Even lowly combat armor will help you survive a shot or two early on.