The Jiangmen Underground Neutrino Observatory (JUNO), the first multi-kton liquid scintillator detector, which is under construction in China, will have a unique potential to perform a real-time measurement of solar neutrinos well below the few MeV threshold typical of Water Cherenkov detectors. JUNO's large target mass and excellent energy resolution are prerequisites for reaching unprecedented levels of precision. In this paper, we provide estimation of the JUNO sensitivity to ⁷Be, pep, and CNO solar neutrinos that can be obtained via a spectral analysis above the 0.45 MeV threshold. This study is performed assuming different scenarios of the liquid scintillator radiopurity, ranging from the most optimistic one corresponding to the radiopurity levels obtained by the Borexino experiment, up to the minimum requirements needed to perform the neutrino mass ordering determination with reactor antineutrinos — the main goal of JUNO. Our study shows that in most scenarios, JUNO will be able to improve the current best measurements on ⁷Be, pep, and CNO solar neutrino fluxes. We also perform a study on the JUNO capability to detect periodical time variations in the solar neutrino flux, such as the day-night modulation induced by neutrino flavor regeneration in Earth, and the modulations induced by temperature changes driven by helioseismic waves.