Understanding what environmental conditions prevailed on early Earth during
the Hadean eon, and how this set the stage for the origins of life, remains a
challenge. Geologic processes such as serpentinization and bombardment by
chondritic material during the late veneer might have been very active, shaping
an atmospheric composition reducing enough to allow efficient photochemical
synthesis of HCN, one of the key precursors of prebiotic molecules. HCN can
rain out and accumulate in warm little ponds (WLPs), forming prebiotic
molecules such as nucleobases and the sugar ribose. These molecules could
condense to nucleotides, the building blocks of RNA molecules, one of the
ingredients of life. Here, we perform a systematic study of potential sources
of reducing gases on Hadean Earth and calculate the concentrations of prebiotic
molecules in WLPs based on a comprehensive geophysical and atmospheric model.
We find that in a reduced H$_2$-dominated atmosphere, carbonaceous bombardment
can produce enough HCN to reach maximum WLP concentrations of $\sim
1-10\,\mathrm{mM}$ for nucleobases and, in the absence of seepage, $\sim
10-100\,\mathrm{\mu M}$ for ribose. If the Hadean atmosphere was initially
oxidized and CO$_2$-rich ($90\,\%$), we find serpentinization alone can reduce
the atmosphere, resulting in WLP concentrations of an order of magnitude lower
than the reducing carbonaceous bombardment case. In both cases, concentrations
are sufficient for nucleotide synthesis, as shown in experimental studies. RNA
could have appeared on Earth immediately after it became habitable (about
$100\,\mathrm{Myr}$ after the Moon-forming impact), or it could have
(re)appeared later at any time up to the beginning of the Archean.