Nevado was born in Madrid and grew up in Spain. She was the first scientist in her family. At high school she was inspired by her chemistry and physics teachers to pursue a career in science. She eventually studied chemistry at the Autonomous University of Madrid, and earned her bachelor's degree in 2000. During one summer holiday she worked at the Menéndez Pelayo International University, where she met international students and realised the scientific community was global. She remained at the Autonomous University for her doctoral research, where she worked on organic chemistry and the cyclisation of enynes that had been catalysed by gold and platinum complexes. After earning her doctorate, Nevado moved to the Max Planck Institute for Coal Research, where she worked as a postdoctoral fellow with Alois Fürstner. Her postdoctoral research considered natural product synthesis. She spent three months working alongside Eiichi Nakamura at the University of Tokyo.