
Other substrates might work
Getting around the rigidity of Von Neumann, mathematical, logic-based, computational approaches, symbolic approaches and traditional computers, other computational substrates like quantum computing, DNA computing, etc. might work and also those that humans have not yet invented, discovered or exploited for this purpose like light, air, memes and information. There must be other substrates, and other viable approaches that are not constrained by mathematics and logic.
Information as a substrate
Narrowly, the only existing example of general intelligence is the human brain and the basic requirements of AGI are self-replication and self-improvement. Considering self-replication, there are many examples of more effective self-replication than humans, for example, memes, disease and microbes. Considering self-improvement, memes also self-improve more effectively than humans as they are refined through repetition, and have the unbounded ceiling for improvement of true AGI.
Taking advantage of the self-reproducing and self-improving properties and using memes and information as a novel computing substrate might be one way of extending AGI progress.
Information as a substrate could be developed symbiotically with a very broadly applicable new understanding of the laws of physics based on information and entropy as opposed to mass and energy.