Total solar eclipses occur because the Moon and the Sun have the same apparent size in Earth's sky — the Sun is about 400 times wider than the Moon, but the Moon is about 400 times closer.
It's my understanding that the Moon is currently receding from the Earth at about the rate our fingernails grow (about 1.6 inches, or 4 centimeters, per year). Lunar retreat rates in the distant past may have been slower than this.
At some point, the Moon will no longer be able to fully block the Sun. (This question on StackExchange addresses the period from now onwards; one solution offered is that the Earth will have its last total solar eclipse in about 600 million years.)
However, what I'm interested in is determing the total duration of that period when it will ever be possible to perceive the Sun's corona (and other effects such as Baily's beads) from Earth by means of a total solar eclipse. This requires knowing both how long it is until the last eclipse will occur (~600 million years) and the time that has elapsed since the first such event happened. Note that the critical period I'm trying to discover is that window of time during which the apparent sizes of the Sun and the Moon, as seen from Earth, are approximately the same size, as they are now.
(In case anyone's interested, my reason for asking this is to try to determine the probability that we humans should have evolved at that point in time when it's possible to perceive a total solar eclipse, to further a pet theory of mine that suggests that it may not be a coincidence.)