I have no problem with the scientific method (a method of research in which a problem is identified, relevant data are gathered, a hypothesis is formulated from these data, and the hypothesis is empirically tested) but my issue is that when we get to the discussion of the age of the earth we can get to the point of hypothesis but cannot test it empirically. Neither young earth or old earth people can prove the age of the earth using the scientific method since that would mean we would have to replicate the formation of the world...not possible. That is when we need to switch to other forms of evidence such as historical writings...the scriptures come to mind.
And yes God does want us to know why things work. That is why He told Adam to have dominion over the earth, this would suggest that Adam should study the earth to be able to use it to the best of his ability (science).
The problem again is that we tend to make assumptions based upon what we want to believe. The dating techniques that I have studied all are based upon assumptions that can not be scientifically tested...and even several of those techniques give us a young age of the earth. Science can not answer every question we have about our existence, to try and apply science to everything would lead us into what is called scientism.
From what I have seen in science that can actually be tested I see the handy work of God and a validation of scripture, which leads me to accept the rest of scripture as reliable in areas that science cannot answer.
The Sun, burning primarily H to He and up through the C12 cycle, is roughly ~5 billion years old, the age of which is known by thermonuclear fusion, which is what the H-Bomb was, so we understand "it" well enough for this.
Earlier, more massive, hence hotter fusion events making them shorter-lived, totals well for ~13by for the Milky Way, which can be optically (the science of “optics”) checked by all other known radiant material in the visible universe, and which by the observed rate of its expansion is itself is not so much older.
There’s also better geophysical evidence for the Earth having formed ~4.5by ago from these same principles, which are much simpler than for the “young Earth”.
This comes not from "assumptions based upon what we want to believe", but from simple analysis of what's there.
Science and God need be studied together.