I believe it’s possible, but only on a singularly and fleetingly rare occasion. In many instances throughout history, people have discovered a new technology by accident and its first use came about without any prior scientific research.
I believe prehistoric cave dwellers may have discovered the benefits of cooking in such a way. Tens of thousands of years ago, perhaps, some cave people were sitting around a fire eating raw meat from a fresh kill. Suddenly, one of the hunters accidentally dropped their slab into the fire. After fishing the food painstakingly and cautiously out of the blaze, the cave person soon discovered that the meat was easier to chew and tasted better.
The above example is a one-time example where people used a technology without science. From then on, the cave dwellers relied on the observed knowledge or ‘research’ that fire makes food tastier and easier to eat and purposely began using the fire to cook their meat.
Yes, I believe technology can exist without science, but only by accident!