The first eukaryotic cells appear in the fossil record around 2.7 billion years ago (bya). These early eukaryotes were likely single-celled organisms and are represented by fossils of acritarchs, which are organic-walled microfossils of uncertain biological affinity.

However, there is evidence suggesting that eukaryotes may have evolved even earlier, possibly around 3.5 bya. This evidence comes from:

* Biomarker analysis: Specific molecules found in ancient rocks suggest the presence of eukaryotic-like organisms even before the first fossil evidence.

* Genetic analysis: Comparisons of genetic material between different organisms indicate a much older origin for eukaryotes.

Therefore, while the first concrete fossil evidence of eukaryotic cells dates back to 2.7 bya, their origin may be much earlier, likely between 3.5 and 2.7 bya.