Descartes' 'cogito' axiom reduces to 'I Am' and he could have just said this for the same effect. As the poet Paul Valery says, 'Sometimes I think, sometimes I Am'.
If you check out the Bible Genesis 3 you'll see that God calls himself 'I Am'. ('Tell them 'I Am' sent you'). For the mystic this is the state of 'I Am' that is prior to thought. This 'I Am' is proved by 'I think' but if we stop thinking it remains.
Regarding the point Omar makes about Buddhism. Intentional consciousness is not 'I Am' but by definition is directed elsewhere. If we begin to see that the 'I Am' of our deepest consciousness is independent of intentional consciousness then we are beginning to see the distinction between self and Self that is so endlessly discussed in mysticism. Take away thoughts and concepts and the self evaporates to reveal the Self, which would be the 'I Am' of the Grail experience and the unchanging Reality that is the source of our 'self'.
Are the assumptions implicit in "cogito ergo sum" therefore justified? I would say there are no assumptions. Perhaps he assumes the reality of the 'I' when he need not but the axiom works anyway. I'd rather say he overcooks the goose since it would be unnecessary to think in order to to be.
If he assumes the reality of the individual 'I' of the self then this is not a justified assumption but it would not matter much. If he simply notes its appearance than this would be enough to prove 'I Am'. The subtlety for a Buddhist would be that the 'I' of 'I think' would not be the same as the 'I' of 'I Am'. They would be respectively the self and the Self. Even so 'I think' would prove 'I Am' since the former would be dependent on the latter.
There would be no 'primordial duality'. This phrase would be an oxymoron. Intentional consciousness would not be primordial. What would be primordial is the unity of consciousness and for this we would have to abandon dualism for non-dualism. The fist duality would be created with the first instance of intentional consciousness, which would be emergent and reducible in metaphysics.
This is a rather rushed and possibly unrigorous sketch of the answer given by the 'mystical theology', the 'primordial cosmology' or 'Perennial philosophy, for which 'I Am' would be fundamental.
"So does this mean that before I can doubt, or think, I must first implicitly or explicitly declare: "I am"?" It seems to me the answer is yes, well spotted, and I'd suggest this is an idea that deserves a lot of thought.