Like all big names in science, she was at the right place at the right time and with the right interest and passion.
Notably, the man she married, Pierre Curie, happened to be a the world master at precisely the technique that she needed to carefully measure radioactivity: he had the most precise electrometers in the world, which allowed to detect small amounts of radioactivity via the ionization of air by radiation . These used piezoelectricity, which Pierre Curie co-discovered with his brother.