No that’s not what happened. Obama came up with a toothless proposal and once ACA was passed he didn’t push further because he didn’t want to piss of the AHA.
So it languished for 6 years with no movement. Trump came in a added it with an executive decision, and it was then that there were legal challenges that were denied. And that’s how we got here.
Like I said, Trump is the worst president of all time but give him his dues when he deserves them. This is one of them.
It was finalized during the Trump administration, but in no way should he get 100% of the credit.