I agree a cab is probably faster but just so you know, it's going to cost you around 35.00 dollars. At that early in the morning, the total drive time should be ~25 minutes.
You could be right but I think you are estimating high on the price (It's nearly that to get to the suburb I live in, 15 miles away!) and time (roads aren't usually terrible yet at that time). Still - it's reasonable to prepare for those numbers, just in case.