If ryuchido was discovered through juugo..

[Hagoromo Itachi]

Then by whom was myouboku Mt. discovered?Shikkotsu forest discovered?Did hashirama study sage mode from snake sage as his symbol is exactly the same one as the one on juugo's hand?

 

[The Necromancer]

Well Hagoromo probably knew about Myaboku, seeing as how he was buds with the Elder Toad Sage.

Hashirama's Sage Mode is Slug Sage Mode (let's be real), but we don't know how their forest was discovered, or when, or why.

 

[Rikudou Tobi]

Ryuchi's senjutsu was just connected to juugo's clan by senjutsu. The way it was explained seems like coincidence because it wasn't specifically written in the manga that the clan found the cave.
Or at least from what I remember.

Hashirama's Sage mode was something passed down in his clan. There is no slug Sage mode nonesense, that fanfic shit will never happen.

 

[Tyrance sasuke]

This makes sense as hashirama's sage mode origin wasn't explained so it might be juugo's sage mode and I checked what he stated and yes; juugo's symbol is exactly the same as hashirama's and sakura's.