I searched for be oblivious to in Thesaurus but it only has synonyms of ignore (to disregard intentionally). I'm looking for something more silimiar to "to not to know".
Truth be told, he __ the answer himself.
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How about overlook or miss?
overlook: to look past : miss
miss: to fail to comprehend, sense, or experience
Truth be told, he overlooked the answer himself.
Truth be told, he missed the answer himself.
In both of these examples, he simply didn't see or notice the answer. No intentionality involved.
Note: @Irhala mentions miss in a comment.
unaware: not knowing that something exists, or not having knowledge or experience of something: I was unaware of the risks involved. Bowman was unaware that the car was gone.
Truth be told, he was unaware of the answer himself.