At a rough estimate,how long could a neutrino travel before striking a particle which would absorb it,& are there any neutrinos from the early days of the universe still wandering about?
So this estimate of mean free path is more than a light year of lead! A fairly common qualitative statement in physics texts is that the mean free path of a neutrino is about a light-year of lead. Griffiths makes the statement "a neutrino of moderate energy could easily penetrate a thousand light-years(!) of lead." This cross section can also be used to estimate the number of events which can be expected in a given size of detector.
The cosmic neutrino background is still around, and is estimated theoretically:
The CNB is a relic of the big bang; while the cosmic microwave background radiation (CMB) dates from when the universe was 379,000 years old, the CNB decoupled (separated) from matter when the universe was just one second old. It is estimated that today, the CNB has a temperature of roughly 1.95 K.
This low energy is not detectable in the laboratory, due to the weak interaction of the neutrino, but there is indirect evidence that the estimates are true.