Were there people alive at the same time as dinosaurs?

Yes! They were created on the same day in fact.

Genesis 1:25-31 God made the beasts of the earth after their kind, and the cattle after their kind, and everything that creeps on the ground after its kind; and God saw that it was good.  Then God said, “Let Us make man in Our image, according to Our likeness; and let them rule over the fish of the sea and over the birds of the sky and over the cattle and over all the earth, and over every creeping thing that creeps on the earth.”  God created man in His own image, in the image of God He created him; male and female He created them.  God blessed them; and God said to them, “Be fruitful and multiply, and fill the earth, and subdue it; and rule over the fish of the sea and over the birds of the sky and over every living thing that moves on the earth.”  Then God said, “Behold, I have given you every plant yielding seed that is on the surface of all the earth, and every tree which has fruit yielding seed; it shall be food for you;  and to every beast of the earth and to every bird of the sky and to everything that moves on the earth which has life, I have given every green plant for food”; and it was so.  God saw all that He had made, and behold, it was very good. And there was evening and there was morning, the sixth day. (NASU)

I visited the Creation Evidences Museum in Glen Rose, Texas and saw a fossil of a human foot print that was made shortly before a dinosaur came by and made a foot print partly on top of the human foot print.  It was awesome!

Here is a picture from their site.  My picture did not turn out as good.  Please visit their site to learn more.

Very very interesting video that goes into great detail, worth watching.