The interplay between crystal nucleation and the structure of the metastable fluid has been a topic of significant debate over recent years. In particular, it has been suggested that even in simple model systems such as hard or charged colloids, crystal nucleation might be foreshadowed by significant fluctuations in local structure around the location where the nucleus first arises. We investigate this using computer simulations of spontaneous nucleation events in both hard and charged colloidal systems. To detect local structural variations, we use both standard and unsupervised machine learning methods capable of finding hidden structures in the metastable fluid phase. We track numerous nucleation events for the face-centered cubic and body-centered cubic crystals on a local level and demonstrate that all signs of crystallinity emerge simultaneously from the very start of the nucleation process. We thus conclude that we observe no precursor for the crystal nucleation of hard and charged colloids.