Question

How might it be possible that the water we drink is from the same age
as the dinosaurs?

Answer 1

water is reused. The water we have on earth doesn't actually replenish but rather goes through the the water cycle. The same water that was in the Ground will end up in the clouds making it rain, or in the Ocean. Whether it is condensation, precipitation, evaporation or percolation, it is the same water going through the water cycle.