big bang theory - The Fermi paradox

I think this too broad, but I'll offer the following:

The star Kepler 444 is orbited by several small, assumed to be rocky, exoplanets. Kepler 444 is estimated to be a very old star, perhaps 11 billion years old, with a metal content of about one third that of the Sun.

Whilst the planets around Kepler 444 are small, they are too hot to be "earth like", but there appears to be no reason why planets at larger orbital radii (that are much harder to detect by the transit technique) should not be there.

Thus the answer appears to be demonstrably, at least 11 billion years ago.

However, the limit cannot be much longer than this, since a certain time must elapse between the formation of the first stars in the Galaxy to the enrichment of the interstellar medium with metals. These metals (all elements heavier than He are referred to as such) are required to build a "rocky" planet. While Kepler 444 demonstrates you don't need a solar metallicity, you still need some.

The fastest place this enrichment took place in general was in the Galactic bulge. A burst of star formation probably enriched the ISM in much less than a billion years.

Thus in principle I would say less than a billion years after Galaxy formation and this is probably not much more than 11 billion years ago.

Kepler 444

http://en.m.wikipedia.org/wiki/Kepler-444

http://adsabs.harvard.edu/abs/2015ApJ...799..170C

The second part of your question is hard. It has taken 4.5 billion years "for life like ours" to evolve. Since we don't fully understand the factors that lead to this, the only realistic answer is that it is probable that it takes another 4.5 billion years after the formation of planets for life "exactly like ours" to emerge.