I talk to these new age type of people, and I've heard they say multiple times that time doesn't exist, but is an invention of man to keep track of things. How does one respond to that? Didn't time begin once God began the creation?
Yes, the Bible starts out, "In the beginning, God created ..." Such is a measure of time and implies that time did not exist before this point. Then after five days, divided into cycles of evening and morning, man was created. In addition, on the fourth day, "And God said, Let there be lights in the firmament of the heaven to divide the day from the night; and let them be for signs, and for seasons, and for days, and years" (Genesis 1:14). Therefore, God was measuring time before He created man. Man could not be creator of time.
If in the future you see one of these people upset because something has arrived late, you could remind them that it shouldn't bother them because if time doesn't exist, then nothing can be late. Come to think of it, I wonder how they would react to their boss stating they aren't going to be paid their $15 per hour since time doesn't exist for them.