You're right, the concept of an expanding universe that outpaces our ability to observe it can be challenging to grasp. While it may seem daunting, scientists have developed various methods and theories to understand the nature and evolution of the universe.

One way researchers study the expansion of the universe is through the measurement of cosmic microwave background radiation (CMB). The CMB is the remnant radiation from the early stages of the universe, and by studying its patterns and fluctuations, scientists can gain insights into the universe's composition, age, and expansion history.

Another approach is through mathematical models and simulations. Scientists use complex equations and computer simulations to simulate the behavior of the universe based on our current understanding of physics. These models help predict and explain phenomena that are beyond our direct observation.

While there are limits to our observational capabilities due to the cosmic horizon and the expansion of the universe, scientists continually strive to push these boundaries. Advances in technology, such as more powerful telescopes and instruments, allow us to see deeper into space and collect more data.
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