We can’t really say “who” came up with these concepts. It’s like asking who came up with the idea that there are spirits and deities in nature. Sure, there were philosophers and thinkers who probably did reason their way to a view of rebirth, like perhaps Plato or Pythagoras. But even there, it’s likely that the seeds of the idea were present somehow.
If you want to know about the early history of transmigration and suffering in India, Advaita Vedanta isn’t the place to look. Advaita Vedanta is a kind of scholastic-mystical tradition that grew out of Brahmanism and interpreting the Upanisads within a particular cultural context after the time of the Buddha.
The place to look is in the schools and views mentioned in the EBTs. Jainism, Ājīvikism, other sramana views and schools, and Brahmanism. Brahmanism was not uniform; there were a variety of views, and there were philosophers and so forth within this tradition as well. It’s best to look at the Brāhmana texts as well as the early Upanisads embedded within them (Brhadaranyaka Upanisad and Chāndogya Upanisad are the best places to start). There we also see discussion of rebirth, karma and suffering, as well as talk about liberation, letting go of desire, non-self, etc.
There was probably a gradual shift that had to do with the second urbanization and philosophical insights at the time which led people to consider rebirth a problem that needed solving. Jainism may be the oldest tradition that we can point to and talk about in this regard, though we don’t have a super reliable textual tradition from them in early times.
I recommend you discover this out for yourself by reading the texts that discuss it. A good place to start would be the Brahmajāla Sutta (DN 1) and the Sāmaññaphala Sutta (DN 2). You could add the Potthapāda Sutta (DN 9) as well as theTevijjā Sutta (DN 13) to the list as well. Then there are dozens of other discourses which discuss specific differences between Buddhism and other schools of thought or teachers. But if you engage with DN 1 as if it were a conversation within a dialectic process of cultural and philosophical evolution, then you should be able to gain a better understanding of what contributions Buddhism made from the primary sources themselves.
It makes a big difference if you engage with the material empathetically, putting yourself into the shoes of the voices in the text, and trying to understand what they are saying. Being told a summary of what someone thinks the Buddha contributed is not the same, and it tends to result more in a matter of memorizing a few phrases that made the Buddha special. But that does not do justice to the richness of what the Buddhist and non-Buddhist materials present to us. If we want to learn Buddhism, we have to engage with Buddhism on its terms. Then we can start to apply that to our situation and participate in a living tradition.
Other good places to look are the discourses at MN/AN/SN which specifically reference other teachers, ascetics, or brahmins and their views.
Not sure what this question is asking.
All the best.