As far as I can tell, this House-passed Bill has yet to pass the Senate: https://qz.com/india/1663752/indian-h-1b-holders-may-be-one-...

https://www.congress.gov/bill/116th-congress/senate-bill/386...

Therefore, someone from India can't just "start H1B to green card conversion process."

They can start the process, it just the process won't complete for a few decades :)