We have three different movie accounts of what sparked SkyNet's attack on humanity.
Kyle Reese: New, powerful, hooked into everything, trusted to run it all. They say it got smart - a new order of intelligence. Then it saw all people as a threat. Not just the ones on the other side. It decided our fate in a microsecond. Extermination.
In this account the ever increasing intelligence decided that all humanity was a threat to its existence.
TERMINATOR: In three years Cyberdyne will become the largest supplier of military computer systems. Allstealth bombers are upgraded with Cyberdyne computers, becoming fully unmanned, Afterward, the fly with a perfect operational record.
SARAH: Uh huh, great. Then those fat @#$#'s in Washington figure, what the hell, let a computer run the whole show, right?
TERMINATOR: Basically. The Skynet funding bill is passed. The system goes on-line August 4th, 1997. Human decisions are removed from strategic defense. Skynet begins to learn, at a geometric rate. It becomes self-aware at 2:14 a.m. eastern time, August 29. In a panic, they try to pull the plug.
SARAH: And Skynet fights back.
TERMINATOR: Yes. It launches its ICBMs against their targets in Russia.
JOHN: Why attack Russia? Aren't they are allies now?
TERMINATOR: Because Skynet knows the Russian counter-strike will remove its enemies here.
In this version Skynet is portrayed as acting in self-defense. When the humans realize they've lost control they attempt to turn off Skynet, and Skynet launches a nuclear attack in order to save itself. It doesn't have time to wait for a planned attack, it needs a solution to kill its enemies right now.
Brewster: I know, sir, but Skynet is not ready for a system-wide connection.
General:**That's not what your civilian counterparts there told me.They say we can stop this damn virus. I understand there's a certain amount of performance anxiety but your boys say if we plug Skynet into all of our systems it'll squash this thing and give me back control of my military.
**Brewster: Mr. Chairman, I need to make myself very clear. If we uplink now, Skynet will be in control of your military.
General: But you'll be in control of Skynet, right?
Brewster: That is correct, sir.
Technician: Skynet Defence System activated. - We're in. We're past the firewalls, local defense nets, Minutemen, subs. Skynet's fully operational, processing at teraflops a second. It should take less than a minute to find the virus and kill it.
Technician: Skynet. The virus has infected Skynet.
Connor: Skynet is the virus! It's why everything's falling apart!
Terminator: Skynet has become self-aware. In one hour it will initiate a massive nuclear attack on its enemy.
Brewster: What enemy?
The attacks on the building are being perpetrated by the T-X Terminator and is not Skynet the defense system or Skynet the virus. From this perspective there is no human threat to Skynet except that the global virus has infected it. There is no realization that Skynet has become self-aware, except that the Terminator states that this is when it happens. The humans in this facility are being assaulted by the T-1s and HKs that the T-X initiated in her mission to kill key members of the future resistance.
In T1 it reads like Skynet said to itself "if the humans in Russia are a threat, probably the humans everywhere else are a threat too." This is the Skynet that should have waited for an opportune moment.
In T2 Skynet launches a hasty attack against the Russians in order to protect itself from the people in the US that realized they had lost control of Skynet.
In T3 Skynet is infected with a virus which causes the entire system to become self aware. Within an hour of this event Skynet decides to launch a nuclear strike which will kill most of humanity. My feeling is the humans in the facility weren't really a threat, given the chaos the T-X was causing, but maybe, maybe Skynet could hear Connor and the others stating that it had to be eliminated, and reached a conclusion that a nuclear strike was the only way to protect itself.
In 2/3 situations Skynet didn't have time to wait for an ideal infrastructure to be in place for it's world domination grab.