Brains are low-frequency, energy-efficient, organic, self-reproducing, asynchronous, self-repairing, and extremely highly connected (thousands of synapses). If AGI is defined as "approximate humans", I think its gonna be a while.
That said, I don't think computers need to be human to have an emergent intelligence. It can be different in kind if not in degree.
Just to put some numbers on "extremely highly connected" - there are about 90 billion neurons in a human brain, but the connections between them number in the range of 100 trillion.
That is one hell of a network, and it can all operate fully in parallel while continuously training itself. Computers have gotten pretty good at doing things in parallel, but not that good.