The first one-celled organisms, or single-celled organisms, are believed to have formed during the Precambrian Era, specifically within the Hadean Eon. This period spans roughly 4.5 to 4 billion years ago.

While the exact timeline is still debated among scientists, it's thought that early life forms emerged in the Earth's primordial oceans.

Here's a breakdown of the key eras:

* Hadean Eon (4.5 to 4 billion years ago): This era is thought to have been extremely hot and hostile, with Earth's crust solidifying. It's during this period that the first evidence of life is thought to have emerged, in the form of single-celled organisms.

* Archean Eon (4 to 2.5 billion years ago): This era saw the development of the first prokaryotic cells, which lack a nucleus.

* Proterozoic Eon (2.5 billion to 541 million years ago): This era witnessed the emergence of eukaryotic cells, which have a nucleus. It also saw the development of multicellular life forms.

So, while the exact time of the first one-celled organisms is still being researched, it's generally accepted that they originated during the Hadean Eon, a truly ancient and fascinating period in Earth's history.