  The formation of the extended thin disc is the most spectacular event of our
Galaxy in the past $\sim8$\,Gyr. To unveil this process, obtaining precise and
accurate stellar ages for a large sample of stars is essential although
challenging. In this work, we present the asteroseismic age determination of
5306 red giant branch stars using \kepler{} and LAMOST data, with a thorough
examination of how the age determination is affected by the choice of different
temperature scales and stellar models. Thanks to the high precision of the
asteroseismic and spectroscopic parameters of our sample stars, we are able to
achieve age determination with an average accuracy of 12 per cent. However, the
age determination is sensitively dependent on the adopted temperature scale, as
50\,K difference in effective temperature may cause larger than 10 per cent
systematic uncertainty in the age estimates. Using the ages derived with the
most plausible set of the temperature scale, we study the age distribution of
the chemical thin disc stars, and present an estimate of the formation epoch of
the first Galactic thin disc stars. We find that the first (oldest) thin disc
stars have an age of $9.5^{+0.5(\rm rand.)+0.5(\rm sys.)}_{-0.4(\rm
rand.)-0.3(\rm sys.)}$\,Gyr, where the systematic uncertainties reflect ages
estimated using different stellar evolutionary models. At this epoch, the
Galactic thick disc was still forming stars, indicating there is a time window
when both the thin and thick discs of our Galaxy were forming stars together.
Moreover, we find that the first thin disc stars exhibit a broad distribution
of Galactocentric radii, suggesting that the inner and outer thin discs began
to form simultaneously.
