Some Neon Genesis Evangelion worldbuilding details for those who like the anime but aside from the main characters ordeals you didn’t understand shit about the anime’s universe foundation. So let’s see.
1 - Before all this, there was a badass primordial race that, for some reason, knew it would become extinct and wanted to spread life throughout the universe as a final legacy. To this end, they created two "technologies": Adam's egg/moon and Lilith's egg/moon. Each of these objects creates a different type of life. Adam creates angels, and Lilith creates humans.
2 - The primordial race decided that angels and humans couldn't live together (just look at them and you'll understand why they can't live together), so they decided that each planet would have only one egg. In case something went wrong, each egg/moon included a bonus object capable of inhibiting its functions, a kind of security system.
3 - Adam's egg fell on Earth, which began to function, and the angels were born here. However, some time later, something went wrong, and Lilith's egg also fell, which was the First Impact that gave rise to our beloved natural satellite we call the Moon. 4 - Lilith's egg also came without a security system, so its functions could not be inhibited. It was left to Adam's egg, which was already functioning, to use its security element and intervene. With only Lilith functioning, humans were born.
5 - Thus, humanity and our little planet as we know it were born. However, after a long time, the SEELE company found Adam's egg dormant. As humans are curious creatures, the moment humans touched Adam's egg, there was a huge explosion called the Second Impact, which completely ruined everything and created the context in which the anime begins. But why did this explosion happen? Precisely because humans emerged from Lilith and cannot coexist with Adam's offspring, so contact between these two different DNA types was something unplanned by the primordial race and should have been avoided at all costs. Basically, what happened was a bug in the egg programming, and everything simply exploded. When something goes wrong, it explodes, simple as that.
From here on, the narrative is easy to follow.