This study aimed to measure the initial portion of signal required for the correct identification of auditory speech stimuli (or isolation points, IPs) in silence and noise, and to investigate the relationships between auditory and cognitive functions in silence and noise. Twenty-one university students were presented with auditory stimuli in a gating paradigm for the identification of consonants, words, and final words in highly predictable and low predictable sentences. The Hearing in Noise Test (HINT), the reading span test, and the Paced Auditory Serial Attention Test were also administered to measure speech-in-noise ability, working memory and attentional capacities of the participants, respectively. The results showed that noise delayed the identification of consonants, words, and final words in highly predictable and low predictable sentences. HINT performance correlated with working memory and attentional capacities. In the noise condition, there were correlations between HINT performance, cognitive task performance, and the IPs of consonants and words. In the silent condition, there were no correlations between auditory and cognitive tasks. In conclusion, a combination of hearing-in-noise ability, working memory capacity, and attention capacity is needed for the early identification of consonants and words in noise.