As an off-topic aside: it sounds as though you are writing a scholarly paper on the subject of consciousness. If I were you, I would definitely not want to convey that I sometimes come to believe things because I want them to be true. It's a form of magical thinking, and is generally incompatible with science and academia. That being said...
I agree that the use of "acceptance" implies that it's established fact that we will understand the brain within our lifetime. Not that we won't--just that there's no consensus on the matter. Also, I changed to past tense to parallel "propelled" in the previous sentence.
Here are some possibilities:
Maybe you feel that the belief was somewhat foolhardy:
The first was coming to
believe, perhaps with undue optimism,
that understanding the brain is
achievable within my lifetime.
Maybe you want to describe the onset of your belief:
The first was coming to
believe, gradually, but with mounting certainty,
that understanding the brain is
achievable within my lifetime.
Or maybe the belief was almost a guilty pleasure:
The first was allowing myself to truly believe
that understanding the brain is
achievable within my lifetime.
You get the idea. This slight re-structuring allows lots of room for tailoring the sentence to your liking.