Due process. The SC reviews the case to see if any errors were made in the trial or appeals process. They don’t judge the facts of the case.
How much do they need? You look at executions in the U.S. in the 1800s, they be convicted and then executed two months later. Look at the Lincoln assassination... Lincoln was killed on April 14, 1865, and all of Booth's co-conspirators were hanged on July 7 of the same year after their arrest, trial and sentencing.
Well into the 20th century, it still only seemed to take a year. So what's with the current 'decades on death row' crap we see today?