I should, therefore, state that science cannot draw out the exact specifics within your dream, as proof that you have actually had the dream you claimed. The individual can know it as 'fact', but anyone else has to trust what is said as that person's experience.
You're changing the goalposts from 'prove we dream' to 'prove a particular dream had a particular content'.
And I don't think we're all that far away from that, tbh.
The biological and psychological mechanics of visual/aural perception and emotional experience are well understood and we are at the early stages of being able to measure them. We just need to be able to collect enough information about the activity, and have models sophisticated enough to interpret it, and we'll be able to say things along the line of 'you saw many people, then you saw one face you recognised, you felt affection'.
The basis for the interpretation is likely to be in part individual to the subject - maps of neurological activity, biometrics and verbal responses taken from the awake individual when presented with certain stimuli.
One thing that a lot of people don't get is that all perception and experience involves the entire body function and sense data. We aren't aware we breath, for the most part. But it can become a conscious process. The idea is that for the most part, this kind of 'autonomic' data, when not brought into awareness-consciousness... it provides a constant background noise, almost a carrier wave for the things which enter our specific awareness. We know we are alive because when we get cold, we feel cold.
The standard thought experiment has been the 'Zombie'. Could you have an organism or machine that wasn't conscious but responded in the same way as one that was.
My view is that this takes us away from the reality of consciouness. It specifically invites us to concieve of it as something hidden, separate. From there, it's hard to work your way back to neurology, calcium channels and proton gradients.
My preferred alternative is to ask, could we preserve a brain in a working state apart from a body? There appear to be specific reasons why we can't feed and maintain it's activity. From this you can make the inference that a self-sensing organ like the brain is not working in isolation. The constant flow of chemical and electronic energies extend to the whole organism. So they underpin the function we call 'sense'. One function of autonomic systems in the brain is to maintain normal operating condition of the organism. We can recognise that we have more 'senses' than vision/touch/smell(taste)/sound/heat, and these are mostly dealing with internal operation.
So take that as your bottom block of consciousness, a subtle awareness of internal the state of things, and work from there, through the simplest organisms that have similair mechanism, through mammalia, and you see extra blocks and and complexity being added, that correspond to mechanisms we have, that cause the same behaviour as those mechansims do in us when presented with appropriate stimuli.
The only way to make sense out of that seems to be to say, consciousness is absolutely not an all or nothing phenomena. There are 'layers', and 'modules' that create more 'complete' consciousness. At the 'more complex' end, we find layers that deal with 'autobiographical' memory, abstraction, reflection - although for my money, they are probably not divisible concepts. When you have a memory of being you some time in the past, that gives you a clearer sense of a self that persists through time.
The ability to abstract and reflect on such experiences is one thing. Having a language that offers you the tools to describe that experience in a manner that can be corresponded to the phenomenoligically derived language of science, is another.