You must be registered for see images
This would indeed be the most logical approach going on the idea of descendants.
Now, to be completely fair, it is good to note that it is not IMPOSSIBLE for the belief you are debunking to be untrue... this is because, while Shinobi Clans may not have existed... family clans, or family units still would have. The Uzumaki with Fuinjutsu take on a more Priestly Class- Like demeanor. The Hyuga have notably kept to themselves (old/archaic fighting style, were mentioned to be Konoha's oldest clan, notably keeping separate from Konoha as a collective). They appear more ancient and rudimentary compared to all of the other clans... nevertheless...
Considering the notion of "No Clans" during the sage's time, the fact that Uchiha and Senju formed from the Elder/Younger Son's
descendants, and the idea that the Uzumaki are
blood relatives of the Senju, I'd say most likely the four clans all owe their roots to the Elder and Younger son.
The key to note is that Obito doesn't say the Elder and Younger Son formed the clans and their names, but instead their ANCESTORS did. Ancestors is a very vague term which could be an immediate, or several hundred generations. With that... I'll continue,
Elder Son: Hyuga-Uchiha
It has been rumored that the Sharingan derived from the Byakugan... this is most likely a falsity, but instead both eyes developed from the Elder Son's Dojutsu. We have an unknown gap between the Elder Son, and his descendants officially forming as "Uchiha". As such, it is likely that there was a separation. One generation or member of a generation, decided that fighting the Elder Son ancestors was not the way to go... even if a difference of opinion existed. This ancestors eyes began to flush out the hatred, and they purified into the Byakugan. The other members (possibly even a majority), continued their hatred, and thus the sharingan continued to form.
Since we do not have specific dates of formation, but the note that Konoha's oldest clan is in fact the Hyuga (it was stated as fact, not Rumor) this means the Hyuga Clan formed first. However, with their reflective and no longer hateful lifestyle, most likely pacified, and kept themselves locked away from the constant wars around them. The Uchiha formed most likely shortly afterwards, and continued war with the Senju. This would help solidify Kakashi's more factual than rumored statement that the Hyuga are Konoha's oldest clan (playing on the words... they were the oldest individual clan in Konoha as opposed to a founding member), and the Sharingan is not formed from the Byakugan considering their relatively different powers.
Younger Son: Uzumaki-Senju
It is noted by Kushina that the Uzumaki are distant blood relatives to the Senju. Now this sounds like something closer to cousins. I would expect a more fatherly or foundational statement to come were the Senju born of the Senju. Likewise, I would expect more of a "We are a branch of the Senju" from Kushina if the Uzumaki formed from the Senju. As such, they most likely formed separate from each other, but from the same genetic ancestors (at one point in time). Since we do not have any age rumors to either clan other than descendance to the Younger son, we cannot logically place which clan is older.
Conclusion: Descent would go Sage ==> Elder Son, Younger Son ==> Oldest Clan- Hyuga, Simultaneously formed from rivalry- Uchiha and Senju, Undetermined but close to the others- Uzumaki
That's my thinking though... If it is true that the Uzumaki and Hyuga do not pre-date the Rikkudou Sennin... this is the most logical plot out of their existence I can speculate. Though, considering exact dates of the clan formations, and the prospect the clans existed, but not as Shinobi Clans cannot be 100% denied, there is always a possibility for a Hyuga/Uzumaki hybrid Sage Child. I just find the four descendant concept more to my liking, and it also better flows with the idea of a structureless anc chaotic time before the Sage defeated the Juubi.