I doubt you can substantiate such claims. Define "the consciousness" and demonstrate that it is something that is present absent a brain.
I can only give you subjective experiences and examples from myself and others, but unfortunately atheists do not trust those.
Many are asking someone for some info, but when they share what they have discovered (upon request), the askers almost imply that the other person is lying.
Scientific evidence is the last step. For evidence of the spiritual, one has to seek the spiritual within and discover for themselves.
Open minded scientists like Einstein (who had read the Bhagvad Geeta - his source of inspiration) have made their discoveries on the basis of faith in a possibility.
A simple example: Say one's Grandma who passed away 8 months ago, visits them in a dream. She is giving them hints about some event and asking them to be careful, and giving her blessings.
Next morning, the dreamer follows the hints and it clearly protects them.
Who is this Grandma in your dream? She has left the body a long ago. No brain.