If a neutrino do not interact with anything and can pass through a light year of lead, how humans manage to detect them?
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The premise of the question is incorrect, neutrinos do interact with other things.
The probability of the interaction is just very low so you need a lot of them to get a few interactions.
Interaction is not a binary always interact or never interact. If you shine visible light on a wooden wall it will not pass through. But instead, use radio waves and X-rays and a large part of them will get through. These are just photons with different wavelengths and they interact with matter in quite different ways.
So radio waves can pass through matter a lot easier than visible light, The same way neutrinos can pass through matter many times easier than radio waves. If the chance of interacting is low enough it can likely pass through a light year of lead. But that does not mean that some neutrons interact with the first meter of the lead, it will only be a minuscule fraction that does that.
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