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The earth has been "proven" to be millions of years old with shaky methods. We know for a fact that radiometric dating does not always work. For example, a rock sample from the newly formed 1986 lava dome from Mount St. Helens was dated using Potassium-Argon dating. The newly formed rock gave ages for the different minerals in it of between 0.5 and 2.8 million years. Mount Ngauruhoe is located on the North Island of New Zealand and is one of the country’s most active volcanoes. Eleven samples were taken from solidified lava and dated. These rocks are known to have formed from eruptions in 1949, 1954, and 1975. The rock samples were sent to a Geochron Laboratories in Cambridge, Massachusetts. The “ages” of the rocks ranged from 0.27 to 3.5 million years old. It seems to me that a scientist could take a rock from an unrecorded source, date it at millions of years, and say that's when it came from. But they have no evidence of that.
Another example of the faulty idea of millions of years: New studies have provided evidence that radioactive decay supports a young earth. One of the studies involved the amount of helium found in granite rocks. Granite contains tiny zircon crystals, which contain radioactive uranium, which decays into lead. During this process, for each atom of uranium decaying into lead, eight helium atoms are formed and migrate out of the zircons and granite rapidly. The decay of uranium into lead is a slow process (half-life of 4.5 billion years). Since helium migrates out of rocks rapidly, there should be very little to no helium remaining in the zircon crystals. Yet, there is still a large amount.
As for religion and science not going together; I'm afraid I have to disagree here too. 
Those looking at the world with a religious view have the same facts as those looking at it with a scientific (with zero religion involved) view. The difference is how they interpret the facts, and that starts with their presuppositions. A Christian is presuming that God created everything (which can't be proven, meaning one must use faith to believe this). Anyone looking at the facts without being a Christian (or any other religion, I suppose) would assume things like evolution, or the big bang to be true (which can't be proven, meaning one must use faith to believe this). It comes down to believing in something that cannot be proven to come to the conclusion of something like an old earth or a young earth. You say that science is about facts, religion about faith, but I find it takes an ton of faith to believe some of the things the scientific world tells me, like evolution (no proof, therefore requires faith to believe in.). The only suggestion I have is to decide which one is more believable.
Lastly (wow, this is long), I'm afraid I can deny the universally accepted ages of the universe, because that's based on a presupposition I don't share. It's not universally accepted either; it's accepted by the majority of the scientific community and the majority of those with no religious ideas. I'm hard-pressed to say that could be considered universally accepted. On your point that we simply have to trust the experts to do their jobs, that's very true. It is a scientists job to give us a scientifically proven explanation to something. Just like it's a police officers job to treat all races fairly, a carpenters job to build the framework right, and an electricians job to properly wire the house. There have been cases where all of these people don't do their jobs right; why can it not be the same with a scientist? Because they're in that field, they are less prone to making mistakes? No. While you have to trust the people to do their job, you have to accept that they won't always do it correctly.
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) Happy discussion!