Currently, most research done in artificial intelligence focuses on neural networks, which have been successfully used to solve many problems. A good example would be DeepMind's AlphaGo, which uses a convolutional neural network. There are many other examples, such as Google Translate, which uses transformers, or DQN, which has been used to play Atari games.
So, are any of the variants of neural networks the only way to reach "true" artificial intelligence (or AGI)?
If by true AI, you mean 'like human beings', the answer is - no-one knows what the appropriate computational mechanisms (neural or otherwise) are or indeed whether we are capable of constructing them.
What Artificial Neural Nets (ANNs) do is essentially 'nonlinear regression' - perhaps this is not a sufficiently strong model to express humanlike behaviour.
Despite the 'Universal function approximation' property of ANNs, what if human intelligence depends on some as-yet-unguessed mechanism of the physical world?
With respect to your question about "the only way": Even if (physical) neural mechanisms somehow actually were the only route to intelligence (e.g. via Penrose's quantum microtubules), how could that be proved?
Even in the formal world of mathematics, there's a saying that "Proofs of non-existence are hard". It scarcely seems conceivable that, in the physical world, it would be possible to demonstrate that intelligence could not arise by any other mechanism.
Moving back to computational systems, note that Stephen Wolfram made the interesting observation in his book 'A New Kind of Science' that many of the apparently distinct mechanisms he observed seem to be capable of 'Universal Computation', so in that sense there's nothing very particular about ANNs.
It depends on what you consider "true artificial intelligence". But this probably means to be able to think like a human - and perhaps, do so in a more rational manner, as in the human brain emotion comes before ratio.
It would seem that a neural network, or a genetic algorithm that evolves neural networks, is the closest way - mimicking humans.
However, the traditional counter-argument to this is that we tried to do the same with flight. We tried to copy nature, mimick the birds - trying to fly by flapping wings. But eventually we made airplanes that did not rely on flapping their wings.
In AI, there are far more variables than in aerodynamics. So it is quite likely that a human-like intelligence can be attained by other methods than neural networks.
In the end, neural networks are one approach to machine learning. There are others, all governed by the rules for what can and cannot be learnt. (There is a field called Computational Learning Theory that covers this).
Although it is possible to extend learning systems beyond what can be learnt according to COLT, this means that such a learning system - neural network or otherwise - is essentially flawed, and will draw wrong conclusions at one point or another.
To have any chance at answering this, you'd first need a rigorous definition of "true artificial intelligence", which we don't have. And even if you had that, the best answer would probably be "nobody knows." We don't even understand exactly how human intelligence (which is probably the best model of intelligence we have available to study) works. What we do know (or think we know) is that ANN's are at best a very superficial replica of brain function. It may turn out that they're absolutely the wrong path to achieving "true artificial intelligence" although I expect most people would be surprised if that turned out to be the case.
What probably wouldn't be so surprising would be if some other technique emerged which is better than ANN's, OR if it turns out that you need an ensemble of techniques. Personally I think it's close to self-evident that the brain works largely in a probabilistic fashion, but it's also clear that we do sometimes use symbolic processing / deductive logic / rules / etc. And right now, ANN's don't give you much in the way of reasoning, deduction, etc. So we may ultimately find that we have to combine a probabilistic approach like ANN's with other techniques - maybe Inductive Logic Programming or something of that nature.
