A laboratory detection of a sterile neutrino could provide the first indication of the evolution of the Universe before Big-Bang Nucleosynthesis (BBN), an epoch yet untested. Such "visible" sterile neutrinos are observable in upcoming experiments such as KATRIN/TRISTAN and HUNTER in the keV mass range and PTOLEMY and others in the eV mass range. A set of standard assumptions is typically made about cosmology before the temperature of the Universe was 5 MeV. However, non-standard pre-BBN cosmologies based on alternative assumptions could arise in motivated theoretical models and are equally in agreement with all existing data. We revisit the production of sterile neutrinos of mass 0.01 eV to 1 MeV in two examples of such models: scalar-tensor and low reheating temperature pre-BBN cosmologies. In both of them, the putative 3.5 keV X-ray signal line corresponds to a sterile neutrino with a mixing large enough to be tested in upcoming laboratory experiments. Additionally, the cosmological/astrophysical upper limits on active-sterile neutrino mixings are significantly weaker than in the standard pre-BBN cosmology, which shows that these limits are not robust. For example, in the scalar-tensor case the potential signal regions implied by the LSND and MiniBooNE short-baseline as well as the DANSS and NEOS reactor experiments are entirely not bound by cosmological restrictions. Our work highlights that sterile neutrinos may constitute a sensitive probe of the pre-BBN epoch.The cosmological evolution of the Universe before its temperature was T = 5 MeV is unknown because we have not detected so far any remnant from it. The earliest cosmological remnants are so far the light nuclei produced during Big Bang Nucleosynthesis (BBN) and if the highest temperature of the radiation-domination epoch in which BBN happened was just 5 MeV, BBN and all the subsequent evolution of the Universe would be unchanged [1][2][3][4][5][6]. Assumptions are made about cosmology to compute the relic abundance and momentum distributions of dark matter (DM) particles which are produced in this pre-BBN epoch. The standard assumptions are that the Universe was radiation-dominated, that only Standard Model (SM) particles are present and that no extra entropy in matter and radiation is produced. We call this set of assumptions the standard pre-BBN cosmology, which is an extension at higher temperatures of the standard cosmology we know at lower temperatures, T < 5 MeV. However, cosmologies based on alternative assumptions are equally in agreement with all existing data. The pre-BBN cosmological evolution could drastically differ from standard in some well motivated theoretical models, e.g. some based on moduli, extra dimensions or quintessence. A non-standard cosmological evolution, consistent with all existing bounds, could drastically affect the properties of any relics produced before the temperature of the Universe was 5 MeV. Detecting any relics sensitive to the pre-BBN cosmological history will open a new window into this yet unexplored epoch. Th...