I think that’s a very interesting question, something I have wondered myself. Before I start to try to answer your question, I want to mention that I am not an expert in the field of Paleo-ethology or statistics which both would be beneficial in order to give you an accurate answer. However, I will do my best to give you a satisfying answer.

There are two ways to your question. The first take is that dinosaurs might have still gone extinct due to natural climate change including movement of the tectonic plates, volcano eruptions etc., or they might evolved in a way that you would not recognize them as dinosaurs as we know and love them today. However, that is not as much fun to think about so let’s have a look at the other side.

During the Cretaceous period before the Cretaceous–Paleogene (K–Pg) extinction event which you mention in your question, mammals which humans are part of already existed and thrived throughout the world, so the notion that only small mammals where able to evolve during the dinosaur period is only partly true. So, in theory the evolution that led to the genus homo could still have taken place even with dinosaurs being present. Would they however been able to survive and evolve further to give rise to homo sapiens? It is another question.

Evolution is a fascinating mechanism that somehow not only gave us this massive biodiversity that we see today but it is also responsible for the natural extinction of several millions of species throughout the history of life on Earth. Whether you survive or go extinct is all about how quickly you can adapt to external changes. We usually call that phenomena natural selection. What I am trying to say is that if dinosaurs were alive while the evolution of the human being started, we, the species of homo sapiens, might have adapted/evolved according to there presence. For example, we might have not left the safety of trees and would still have a tail or long arms instead of long legs. Another thought is that during our history we had to battle/overcome and live with pretty scary mammals that grew not as tall as a Tyrannosaurus Rex or an Allosaurus but they where big enough to compete with the Utahraptor or the Deinonychus, often mistaken for a Velociraptor. I am thinking about the famous saber-toothed cat (Smilodon) or the big short-faced bear (Arctodus).

In fact, there is increasing evidence that the presence or arrival of humans led to an increased rate of extinction for big mammals such as the ones I mentioned before. So, in that sense human beings might not only have evolved while dinosaurs were still alive but they might even have driven them to extinction in the same way as we did for several other big mammals such as the mammoth or the giant ground sloth.