They came from the stars. We didn't notice.
The Squid Father came to Earth decades before the war. He knew if the takeover of Earth was too fast, then the humans would be united. The trick was to conquer one person at a time. So, he took over the body of an unsuspecting college student, invading through the mouth and living in the stomach of his Puppet victim. Born pregnant, the Squids would pass their eggs through the human host, causing the human to create a nest by vomiting up eggs. Then the Puppet would lure unsuspecting humans into each nest, spreading the gospel. Each nest expanded the hive. Those hives into an invasion. Then one day, decades later, we noticed. They broadcasted their intentions. Those that would not submit to the Gospel would be consumed as fuel for the hives.
The Puppets took the cooler parts of the world quickly, being biologically predisposed to thriving in cooler climates. Much of the developed world was gone in the first year of the war. Early on, the newborn Squids were only able to do the simplest of tasks in their Puppet. This resulted in waves of Puppets stampeding against human defenders. Enough of those defenders had trouble massacring the waves and were overrun. In the early years of the war, only the most brutal and violent survived. Soon, the resistance was left down to those humans stubborn enough to fight in the hottest climates. When trapped in one hundred plus temperatures for too long, the Puppet host body would reject the Squid that was living in its stomach, causing blood to pour out the nose and the Squid to climb back outside the mouth.
The War lasted 6 years, until the Hive King was destroyed, causing the link between all of the Puppets to be severed and the hosts all died from brain aneurysms.