Honestly....this is actually a good theory. There is one little note I would add as well one potential problem to your theory:
Note: If Sasuke is Ashura + Indra, then Madara had to be as well. Also, just to add to your theory and my note:
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Problem: Going along with the same premises in your theory, shouldn't Sasuke have awakened the Rinnegan once Hashirama gave him some of his Chakra? As you showed, Madara mixed Indra's with a part of Ashura's Chakra and awakened the Rinnegan. HOWEVER, what you did not highlight is important, "...And that brought out my [So6P] Chakra."
If Hashirama gave Sasuke his Chakra (which Hashirama was an Edo-Tensei), the So6P/RS Chakra should have been awakened/been brought out and Sasuke would have a Rinnegan way before this:
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So...we have established that Madara and Sasuke have a much stronger blood connection than just being from the same clan. And most likely what Madara noticed in Sasuke was both of them being Inheritor's of Indra's Chakra.
We also know there is a missing link. Madara states in the link above that he has BOTH the Senjutsu of the Six Paths and the Rinnegan. HOWEVER, he only received the Senjutsu of the Six Paths AFTER becoming the Ten-Tails Jinchuriki (like Obito before him). Naruto gained that power because he was already left with a part of all the 9-Tailed Beast's Chakra.
I don't have all that much time to write everything I wanted to, so I will finish with this:
I think it is a good theory, but clearly Sasuke's Rinnegan was NOT awakened by the method Madara used AKA mixing both Indra's and Asura's Chakra which brought out the Sage's Chakra. It is clearly shown that Sasuke was given Hashirama's cells -
from BOTH Hashirama himself and Kabuto and still did not awaken the Rinnegan the same way as Madara, which eliminates your conclusion:
"the rinnegan itself is the prove of the existence of both ashura and indra's powers within sasuke (senju and uchiha)"
P.S. - Since Sasuke received or seems to have received Hashirama's Cells from both Kabuto and Hashirama, wouldn't it make sense - especially from Kabuto, that Sasuke would be granted Wood Release or one of the other several powers Hashirama's Cells granted?