Early literacy skills serve as the best precursors of reading success and risk indicators of the double deficit and triple deficit hypotheses according to the spelling consistency of languages. Our study analyzes the predictive value of phonological awareness, naming speed, and orthographic skills for early reading in Spanish. Participants included 362 Spanish children aged 4 to 5 years. We used data analysis to examine the relationships between these precursors and fluency through a structural equation model and investigated the risk indicators of poor reading performance according to the double deficit and triple deficit hypotheses using binary logistic analysis. Our research delimits a model for the Spanish language that emphasizes the predictive value of phonological awareness, letter-naming fluency, and knowledge of graphemes in early reading. Letter-naming fluency is the best precursor to early reading experiences, and poor early reading performance in children is explained by deficits in phonological awareness, naming speed, and visual orientation. Our findings confirm the risk indicators of the triple deficit hypothesis in the early learning of reading in Spanish.