No — the math does not work. Humans and non-avian dinosaurs were separated by 66 million years of evolution. This is not a matter of opinion or incomplete fossil records; it is basic paleontology and radiometric dating.
Non-avian dinosaurs (T-rex, triceratops, stegosaurus) went extinct 66 million years ago when an asteroid hit the Yucatán Peninsula. Mammals existed alongside dinosaurs, but they were small — mostly rat-to-squirrel sized. Humans did not evolve until roughly 300,000 years ago. That is a gap of 65.97 million years.
For context: the entire time humans have existed — every civilization, every war, every technological advancement — is less than 0.0005% of the time since dinosaurs walked the Earth.
Hypothetically, early humans (without fire, weapons, or complex tools) would have been easy prey for mid-sized theropods. Large herbivores like sauropods would have ignored us. The real issue: we could not have evolved into modern humans in an ecosystem still dominated by dinosaurs — the evolutionary niches were already filled, and our line of primates needed the mammal-dominated world that only existed AFTER the asteroid.
Pro tip: Birds ARE dinosaurs (avian dinosaurs). So humans do coexist with dinosaurs right now — that robin in your yard, the eagle, the chicken. Evolution did not kill dinosaurs; it transformed them.