The heart of the "Big Bang Universe" is that the universe had a beginning. Not just any kind of beginning; a beginning of not just energy and matter, but also space and time itself. There are space time theorems which imply that there must be an agent outside of space and time that creates our universe of matter, energy, space and time.
Dr. Hugh Ross continues to explain the second feature of big bang cosmology is the continual expansion from the space time beginning. What is means is that the universe gets bigger and bigger as it gets older and older. This happens under laws of physics that remain constant throughout the whole history of the universe, therefore it is something we can prove by direct measurements.
Finally the last principle of the big bang cosmology is that everything is decaying with respect to time.
All these are the fundamentals of the big bang cosmology.