The age of the universe has been determined by three different independent techniques, all of which yield the same age.
And what techniques might those be? Science has never determined it. I'm sure Drs. Snelling, J. Morris, Woodmorappe, and Steven Meyer would love to hear it. Wjhat you left out (conveniently) is that all current techniques assume that the model is correct. As an example, using light to determine age runs into the horizon problem: you assume that all variables remain constant, everywhere. You are left with a hypothesis, but it's not something that can be proved.
So I prefer to go with what CAN be proved: the resurrection of Jesus Christ, and his fulfillment of 365 prophecies attributed to the Messiah. That alone gives me a baseline to "prove all things, hold onto that which is good". And if he is truth embodied in human form, then everything he has said is true.(1 Th 5:21 and John 17:17).
Radiometric Dating, A Christian Perspective[snip] Radiometric dating -- the process of determining the age of rocks from the decay of their radioactive elements -- has been in widespread use for over half a century. There are over forty such techniques, each using a different radioactive element or a different way of measuring them. It has become increasingly clear that these radiometric dating techniques agree with each other and as a whole, present a coherent picture in which the Earth was created a very long time ago. Further evidence comes from the complete agreement between radiometric dates and other dating methods such as counting tree rings or glacier ice core layers. Many Christians have been led to distrust radiometric dating and are completely unaware of the great number of laboratory measurements that have shown these methods to be consistent. Many are also unaware that Bible-believing Christians are among those actively involved in radiometric dating. This paper describes in relatively simple terms how a number of the dating techniques work, how accurately the half-lives of the radioactive elements and the rock dates themselves are known, and how dates are checked with one another. In the process the paper refutes a number of misconceptions prevalent among Christians today. This paper is available on the web via the American Scientific Affiliation and related sites to promote greater understanding and wisdom on this issue, particularly within the Christian community. ...differences still occur within the church. A disagreement over the age of the Earth is relatively minor in the whole scope of Christianity; it is more important to agree on the Rock of Ages than on the age of rocks. But because God has also called us to wisdom, this issue is worthy of study. [/snip]
by Dr. Roger C. Wiens
First edition 1994; revised version 2002