While the 4.4 billion years ago is a guess as to when these processes might have started, the 4.1 billion years ago guess is a better representatoin of current understanding on when the needed building blocks of life evolved.
Before the appearance of self-replicating molecules, there was a crucial phase of chemical evolution where simple organic molecules formed from inorganic precursors. This process, possibly facilitated by conditions on early Earth or through extraterrestrial contributions (like meteorites), led to the accumulation of organic compounds, such as amino acids and nucleotides, setting the stage for the complexity of life.
