Researchers hope it will help shed light on how the universe evolved after the big bang.
The Square Kilometre Array (SKA) - a telescope due to be completed by the end of the decade - will likely be able to make images of the earliest light in the universe.
Thick hydrogen clouds make that difficult for current telescopes.
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The signal astronomers aim to detect is expected to be approximately 100,000 times weaker than other radio signals coming from the sky - for example, radio signals originating in our own galaxy.
Now, researchers led by the University of Cambridge have developed a methodology to see through the clouds and other sky noise signals, avoiding the distortions introduced by the radio telescope.
Their new methodology, part of the Reach (Radio Experiment for the Analysis of Cosmic Hydrogen) experiment, will allow astronomers to observe the earliest stars through their interaction with the hydrogen clouds.
It is the same way experts would infer a landscape by looking at shadows in the fog.
The paper's lead author, Dr Eloy de Lera Acedo, from Cambridge's Cavendish Laboratory, said: "At the time when the first stars formed, the universe was mostly empty and composed mostly of hydrogen and helium."
He added: "Because of gravity, the elements eventually came together and the conditions were right for nuclear fusion, which is what formed the first stars.
"But they were surrounded by clouds of so-called neutral hydrogen, which absorb light really well, so it's hard to detect or observe the light behind the clouds directly."
The new method analyses data from multiple antennas and across a wider frequency band than equivalent current instruments.
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The telescope's construction is being finalised at the Karoo radio reserve in South Africa, chosen for its excellent conditions for radio observations of the sky.
It is far from human-made radio frequency interference, for example, television and FM radio signals.
Professor Dirk de Villiers, co-lead of the project at the University of Stellenbosch in South Africa, said: "Although the antenna technology used for this instrument is rather simple, the harsh and remote deployment environment, and the strict tolerances required in the manufacturing, make this a very challenging project to work on."
He added: "We are extremely excited to see how well the system will perform, and have full confidence we'll make that elusive detection."
The findings are published in the Nature Astronomy journal.