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How did man ever invent fire, without another person telling them?
Fire already existed, long before people existed. So it was a matter of applying a version of what later became called the scientific method - observe, hypothesise, experiment.
I can think of a few reasons why it might have happened.
i) Fire makes heat. It's cold in winter. A small controlled fire would make a cold place warm, better for living.
ii) After a natural fire, people would sometimes find recently dead partially burned animals. Smells edible. Food is in short supply after a lot of the plants your group eats have burned. So someone tries eating it. Works well.
iii) Fire is destructive. If we can make it and control it, we can use it as a weapon.
I can think of a couple of ways how it could have happened.
i) When making stone tools by knapping, sparks might have occurred if a hammer stone was used and it was of the right material. Are those sparks small fires? They look similar. Can they be used to start a small fire? Try getting the sparks into a bit of dry grass.
ii) When rubbing two things together, heat is generated. Fire is hot. If you generate enough heat, will you make fire? Figure out a way of moving one stick against another fast enough to test that hypothesis. It can be done by hand.