Final answer:
The Cosmic Microwave Background provides evidence of a homogeneous universe in its early state, with its uniform temperature reflecting an even distribution of matter and energy.
Step-by-step explanation:
The evidence that the universe was homogeneous during its first 400,000 years comes primarily from the Cosmic Microwave Background (CMB) radiation. The CMB is remarkably uniform in temperature across the sky, suggesting a uniform distribution of matter and energy when it is released. The minute temperature fluctuations observed in the CMB are also consistent with the early formation of structures like galaxies and galaxy clusters, which developed through gravitational attraction over time. This uniformity supports the idea that the universe was in a smooth state and adheres to the cosmological principle, which assumes isotropy and homogeneity on a large scale. The Automated Plate Measurement Galaxy Survey further supports the idea of an early smooth universe by providing observational data consistent with these principles.