Every time I start a game and get the first kill in the game, it freezes.

I5 6500
GTX 1060 3GB
32GB DDR3 1866
Windows 7 x64 Professional

Playing on high settings with Second Wave enabled. Launched from Windows and from Galaxy.

Can someone please inform me, how to get past this?

Somebody had the same problem.

It was caused by the firewall blocking network access. Killing the enemy might trigger achievement and that requires network access. If firewall blocks it, it can cause a crash.

I did have this happen once. I don't have an internet connection to my game machine, so I have always played disconnected, so that shouldn't be a game-breaking bug. (Then again, I don't use a firewall, which would definitely be capable of messing with a game.)

Enemy Unknown is horribly unstable for me, but, for some reason, Enemy Within is good for hours on end. Weird.

(Also this is in Wine so YMMV, but playing with/without Enemy Within might be worth trying)

Not really. Enemy Within is an expansion of the original Enemy Unknown game, hence it has improvements.