I think the linchpin of my belief is recursive self improvement. I think machine intelligences are a different kind of substance with different dynamics than the ones we typically encounter.
I don't think someone will compile the first AGI and presto there is it. I think a long running system of processes will interact and rewrite its own code to produce something, which eventually a reasonable boundary could be drawn to distinguish the system and anyone interacting with the system would say: "this thing is intelligent, the most intelligent thing on the planet". It would have instant access to all written knowledge, essentially unbounded power to compute new facts and information and model the world to as accurate of an approximation as needed to produce high confidence utterances.
I just don't see how a system like that couldn't come into existence one day. Issues around timelines are completely unknowable to me. But I would put a distribution of something like I would be surprised if it happened in the next 50 years and shocked if it didn't happen within the next 1000. Very fuzzy, but it "feels" inevitable.
If a collection of unthinking cells can coordinate and produce the feeling of conscious experience then I can't see what would stop silicon from producing similar behavior without many bounds inherent in biological systems.