Just by spawning ten of them every hour at random places in each of the top 100 biggest US cities (24k daily), between the chaos and disruption, it would be done.
I can keep that rate for 342 years with 3000 million beings, but I think in one year they would be done. Give me 10 million xenomorphs and I can end the USA.
Hell, I can drop some in the biggest military bases and totally disrupt military response.
One per plane (acid blood), I only need 10k xenomorphs and the USAF is gone
Drop about 50 xenomorphs on a single navy ship and it would be EXACTLY the scenarios that are in the movies. Cramped, tight spaces.
You could probably take NYC with about 50k xenomorphs. They're not mindless beasts. They're super intelligent space ninjas that are born to be pure weapons. Even their deaths are dangerous.
Outside the cities, it's forests. Plenty of cover and opportunity for deadly night fighting. Also consider the breeding with local fauna. I mean... A xenomorph Grizzly would be fucking horrible.