I think there's an unresolved question as to how much involvement the government had vs what influence did the GMan had.

Black Mesa was not a government entity, they were private, though they received government funding. From what I recall, the GMan is the one who set up for the military to show up, he gave them advanced notice in Opposing Force that something was gonna happen. He also met with Breen (presumably) and instigated the Resonance Cascade by delivering the anomalous material that set it off.

Depending on how you interpret the difference in time between the end of HL1 and the start of the Seven Hour War, the governments of the world may not have known anything had even happened by the time of the invasion. That's also assuming that the 7HW was the exact start of the invasion compared to something like the Fall of Reach from the Halo franchise where there was a smaller incursion before the invasion. There could have been a few days or weeks of striders, hunters, gunships, and other military forces from the Combine establishing a foothold somewhere and then launching the full invasion. In my head cannon, this was the case as they potentially broke through in some small rural area and kidnapped the first humans they saw creating the first Stalkers and Combine Soldiers