Your problem is simple, modern day science misinterprets the age of the earth and universe. No where does the scientific method allow for discarding any/all data contradicting a theory, but many do it anyway.
http://creation.com/age-of-the-earth
To be fair, 5 years ago, I was where he is now. I have an engineering degree, and all the requisite “science” courses to go along with it. Everywhere along the way, my “education” made the assumptions of old earth and evolution, it was all that was taught, so it was all that I knew, until...
a few years ago I started studying the contradictory evidence, put on “new glasses”, and looked at the evidence cited for evolution/old earth in a new way, and saw where the errors were.