Measuring the solar neutrino flux over gigayear timescales could provide a new window to inform the solar standard model as well as studies of the Earth's long-term climate. We demonstrate the feasibility of measuring the time evolution of the B-8 solar neutrino flux over gigayear timescales using paleo detectors, naturally occurring minerals which record neutrino-induced recoil tracks over geological times. We explore suitable minerals and identify track lengths of 15-30 nm to be a practical window to detect the B-8 solar neutrino flux. A collection of ultraradiopure minerals of different ages, each some 0.1 kg by mass, can be used to probe the rise of the B-8 solar neutrino flux over the recent gigayear of the Sun's evolution. We also show that the time-integrated tracks are sensitive to models of the Sun.