[xefer]

I found this reference in which the abstract provides this definition: "The age of the Solar System can be defined as the time of formation of the first solid grains in the nebular disc surrounding the proto-Sun"

https://doi.org/10.1038/ngeo941

"The age of the Solar System can be defined as the time of formation of the first solid grains in the nebular disc surrounding the proto-Sun. This age is estimated by dating calcium–aluminium-rich inclusions in meteorites. These inclusions are considered as the earliest formed solids in the solar nebula. Their formation marks the beginning for several long- and short-lived radiogenic clocks that are used to precisely define the timescales of Solar System events, such as the formation and evolution of planetary bodies1,2,3. Here we present the 207Pb–206Pb isotope systematics in a calcium–aluminium-rich inclusion from the Northwest Africa 2364 CV3-group chondritic meteorite, which indicate that the inclusion formed 4,568.2 million years ago."

[cbkeller]

Yeah, that's it -- since the first solid material also means the first material we can determine an age of!