The organisation has given a big update on its mission and approved preliminary design plans for the observatory, with work now starting on a "final, detailed design" and the hardware and software.
SPHEREx - which stands for Spectro-Photometer for the History of the Universe, Epoch of Reionization and Ices Explorer - is scheduled to launch between June 2024 and April 2025.
In a press release, NASA explained: "Its instruments will detect near-infrared light, or wavelengths several times longer than the light visible to the human eye.
"During its two-year mission, it will map the entire sky four times, creating a massive database of stars, galaxies, nebulas (clouds of gas and dust in space), and many other celestial objects."
The telescope - which is expected to be the size of a "subcompact car" - is set to be the first NASA mission to create a "full-sky spectroscopy map in near-infrared", capable of observing 102 near-infrared colours.
Project manager Allen Farrington said: "That's like going from black-and-white images to colour."
The first priority is to find evidence of something NASA says could have happened "less than a billionth of a billionth of a second after the big bang".
By mapping billions of galaxies, the hope is NASA will find statistical patterns to explain what happened immediately after the big bang, while the new map will also help look for water ice and frozen organic molecules around new stars.
Another goal is to learn more about galaxy formation, and potentially even discover how some of the earliest galaxies created stars.