The geologic evidence for a warm early Earth is
simply that there are 3+ billion year old (modified)
sedimentary rocks that had to have been deposited in
a liquid environment.
The atmospheric evidence for a warm early Earth
stems from the observed (recorded, for example,
in ice cores and rock samples) isotopic
ratios:
deuterium/hydrogen and 16 oxygen/18 oxygen.
Both of the observed ratios require warmer temperatures.
The geologic evidence for a warm early Mars is
what you think it is: old river and flood channels
observed on Mars! We don't know how old they
really are, though we have some idea from counting
craters that they must be at least 1 billion years
old. And we know they cannot be young anyway because
liquid water cannot exist on Mars today!