Since we are pushing 10 pages and approaching 200 posts … did anyone ever identify the source of the data that the OP requested? (That’s too much Off Topic debate on YEC vs OE Science to wade through).
The short answer is: NO. There wasn't some big get together with the scientists from various fields getting together for a consensus. The modern 13.7 Gyr age is given by the one science that actually studies the history and development of the Universe as a whole: Cosmology. (Much of it comes from one experiment, cross checked by others and various "joint analyses".)
In the early days of rigorous geology it was clear that the time to form rocks was a million years or more, but the ages required a lot of educated guess work (how long does it take for a particular rock formation to accumulate, etc.). Likewise paleontology and evolutionary biology put similar constraints such that the Earth was probably tens to hunderds of million years old, but the values were not precise.
Then with the atomic age came radiometric dating, specifically techniques involving the decay of Uranium. These put the age of the Earth in the 4.5 Gyr (with 0.2 Gyr or smaller error bars) range about 60 years ago and the value hasn't budged since. This gives a *minimum* age for the Universe since the Earth is presumably not older than the Universe. (Unless the Earth is *really* weird.) Radioactivities from meteors and the Moon. Confirm this age.
The other constraints/measurements of the Universe came from the ages of stars and the structure of the Universe. Many of these were boosted in the last 50 years by the development of CCDs to precisely measure photon counts from distant stars, larger and space-borne telescopes, and computer hardware and software to handle the large amounts of data.
On the stellar side, models of the Sun confirmed the age of the Solar System. Then globular clusters in our own Galaxy were measured with thousands of nearly-equal aged stars in each. The H-R diagrams of the stars brightness and surface temperature (color) were compared to the isoschrones of coeval stellar evolution models to get ages from the clusters (and as a bonus the distance). These gave ages for the oldest globular custers in the range of 12-17 Gyr (or so, I'm working from memory). There was some uncertainty to be clear.
On the cosmological side there were a lot of reason to think the Universe was "flat" and in the simple models would mean the Universe would slow down in expansion asymptotically to a halt as opposed to a closed universe that would collapse back, or an open universe that would expand forever. This was supported by some observations and simple models of the Universe. With that notion in place various measurements of the local expansion rate (the Hubble expansion) translated directly to the age of the Universe. The expansion measurement each had error terms and didn't fully agree, so when I learned basic cosmology 30 years ago the "safe" value for the age of the universe was 10-20 Gyr based on the various stellar age and expansion measurements. That would all change in the next decade.
It was increasingly clear that the matter detected by astronomers was not sufficient for the apparent "flat Universe" scenario. The visible matter (bayronic matter) was way short of the amount needed for a flat universe, and even the dark matter (a placeholder name for matter that doesn't interact with light) detected through the motions of galactic rotation and galaxy clusters was not sufficient. There were then 3 kinds of matter: visible, dark, and "missing" where the "missing" matter was needed for cosmology, but nothing else.
This was solved in the late 1990s by the discovery of the acceleration of the Universe by using the brightness of distant Type Ia supernovae. These were further away than their observed brightness would imply. Translating this "accelerating factor" into a cosmology resulted in a "Dark Energy"- an unknown bit of physics that acts like a "negative pressure" causing acceleration of the expansion of the universe. This "dark energy" fit right in the slot of the "missing matter" (after all matter and energy have the same impact in GR) and quickly set the content of the roughly flat universe at about 30% matter (baryonic and dark) and 70% "dark energy".
Then came WMAP, a satellite to measure the fluctuations in the microwave background. It's first year of data released in early 2003 set the age of the Universe at 13.4 +/- 0.3 Gyr by itself and confirmed the flat nature of the Universe. When added to the supernova and other data in a "joint analysis" the age of the Universe was 13.7 +/- 0.3 Gyr. The full data set from WMAP (released in 2012) gives the age of the Universe at 13.74 +/-0.11 Gyr just from WMAP data and 13.772 +/- 0.059 Gyr including all available reported data.
When I was in that class we would have considered it ludicrous to think we could know the age of the universe to 0.5%, but now we do.
