Yes.
Assuming space travel tech that existed in the 1960s.
First, using Saturn V, or N1, rockets, physically collide with a massive asteroid and set it on a collision path to earth.
The asteroid that killed the dinosaurs was only 6 to 9 miles in diameter. I bet we can get something bigger.
Once the sunlight is blocked and crops fail, the mass starvation and total environmental collapse will result in the total and complete collapse of all civilizations.
The dearth of oxygen, due to the death of the vast majority of plant life, will result in humanity basically becoming extinct except for in a few remote locations underground where humans survive off of the heat from local volcanic activity, and the oxygen produced by bacteria, and eating troglobites to survive.
There are probably pockets of plants left near the equator and near jetstreams to help with Oxygen production. Plants clearly survived the Dinosaur killer after all.
By the time the next Ice Age is over, you'll be back in the Stone Age.