The assumption is that since there is already a neural network that “got there” (our brains), we should be able to achieve the same thing synthetically.
We just need to figure out how to train that network.
Neural networks are a simplification of our brains, they are not a replication of it. It is just a modeling method that was inspired by how human neurons work, that's it. It's not 1 to 1 or anything.
Furthermore, neurons alone do not led to consciousness. At the very least, their modulation, mainly by glial cells, is essential as well.
Personally, my money is on quantum coherence within microtubules being the mechanism of conscious experience, with the brain essentially being a quantum/classical hybrid computer.
It may be possible to argue that current work in AI leads to some definition of intelligence, which apparently often is equaled to consciousness by some.
My take it is just unaware intelligence like in Peter Watts’ book Blindsight. A terrific read and a quite scary prospect.