Cosmic Microwave Background
The cosmic microwave background (CMB) is light left over from when the universe was about 380,000 years old. Before then it was a hot, opaque plasma; at recombination it cooled enough for atoms to form and light to stream freely. That light has been stretched by expansion into faint microwaves — the coldest radiation in the cosmos — filling the whole sky. Tiny temperature ripples in it — mapped precisely by satellites — encode the early universe's contents and geometry, and fitting that pattern gives the age to better than 1%: 13.8 billion years.
Before atoms formed, the early universe rang like a struck bell: gravity pulled matter into dense spots, photon pressure pushed back, and the plasma oscillated. Those sound waves froze in when atoms formed, leaving a series of acoustic peaks in the temperature pattern. The first peak's position is a ruler for the geometry of space (it says the universe is flat); the relative peak heights weigh its contents. Add more ordinary matter and the odd (compression) peaks rise while the even (rarefaction) peaks sink — slide the baryon density to see it. Fitting this curve is what pins the age to 13.8 billion years. (Schematic — shows the structure, not exact values.)