Here's a great little calculation that looks easy to have thought of doing oneself, but only in retrospect: plot the number of DNA base pairs (a proxy for the complexity of life) against when that life form arose:
authors put it at 9.7 ± 2.5 billion years ago.
Since that's less than the age of the Earth -- 4.5 billion years, although heavy bombardment didn't stop until 700 million years after that -- life may well have started other than on this planet.
You could wonder if life doesn't need some bottom number of genes in order to exist -- the first self-repliating synthetic cell built by the Ventner Institute has 1.08 million base pairs, which would put it on the right-hand side of the Origin of Earth line in the graph above. The symbiotic bacterium Carsonella ruddii has just 159,662 bp (so log10=5.2, also on the right-hand side of the Earth line), but it sponges off sap-feeding insects so perhaps didn't develop on its own (and neither it nor it host makes the essential amino acid tryptophan, so it may also be sponging off a second host).
In any case you might wonder how something with a million base pairs evolved if something simpler didn't come before it; the authors write "life may have started from systems with single heritable elements that are functionally equivalent to a nucleotide."
Anyway...this paper puts the doubling time for the base pair count at 376 million years, and, it says, the doubling time for "human functional complexity" at 20 years.
There looks to be much more interesting and provactive speculations in their paper, which I look forward to reading.
Speaking (well, writing) of reading, there is a wonderful article in Aeon by Ross Andersen on humanity's deep future, whether humans will go extinct, why a few philosophers are hoping the Mars Curiousity rover fails (it's not for the reason you think), and many other interesting ideas. Definitely check it out.