We'll know that we've reached the singularity when there's a mysterious and superintelligent AI entity with technology and motivations that we as humanity do not understand and have no control over. Not sure why we want that, exactly, but that'll be the big sign.
I want a singularity yesterday, and I would even go as far as to claim that all people have an ethical obligation to build super intelligent AI systems as fast as possible to reduce the maximum amount of suffering through the universe possible in living things.
The moment that we can get viable non-human leadership I will embrace it with open arms. The yoke of human existence is extraordinarily oppressive. Give me Ghost in the Shell style cyberborgs. We are the demiurge.
Of course, the real red pill is to realize that there's many singularities. Can't believe I'm going to link Orions Arm on HN but its relevant here: https://www.orionsarm.com/page/298