Well, AFAIK there's nothing in history that resembles the singularity. We have evolution, but it took a long time. We can claim that computers are faster than evolution, but that's just something we think is plausible. Humans reproduce every 20+ years, so if computers can do it faster, we're going to witness a cyber evolution.

And add quantum computers. Quantum computers have the potential ability to search exponentially growing space just by adding logical qubits. There's no equivalent in nature of quantum computers AFAIK. This doesn't rule out quantum computers.

The other option is biological computers using neural tissue. This doesn't seem as spectacular as quantum computers but still could potentially beat human evolution. I mean, this is not a religious argument. I'm not trying to prove the existence of God. There could be a path to AGI or not. It's more of an engineering question like can you break the sound barrier?

By the way I don't believe in the literal Singularity. There are many hard limits IMO that would prevent it.

TLDR Singularity might be achievable, but maybe not the literal Singularity. Technology could be developed to get us close.