How do we know so many details about Big Bang, but we do not know if Universe is finite/infinite?
By observing the observable universe we can gather a lot of data about the constituents of the universe now and in previous epochs, right back to the cosmic microwave background. This data places quite narrow constraints on viable models of the Big Bang. This is why cosmologists are confident about the details of the Big Bang, certainly from electroweak symmetry breaking onwards.

However, it is much more difficult to make an observation of the observable universe that could distinguish between a very, very large but finite universe and an infinite universe. That is why this is still an open question.