The acquisition of quantifiers is a central topic in cognitive science. The present study investigated the emergence, frequency, and non-target-like production of the universal quantifiers "all," "every," and "each" in child English from a linguistic perspective, based on the data from longitudinal naturalistic observation of 10 English-speaking children and their caregivers. We found that the use of these quantifiers as adverbs or in adverbials generally appeared earlier, and was more frequent, than their use as (pre)determiners in early child English. We also found that input frequency exerts a great influence on some aspects of the acquisition of universal quantifiers, for example, the frequency of the predeterminer "all," but there are still some patterns that cannot be explained by mere input frequency, such as children's initial preference for using universal quantifiers in A(dverbial)-quantification and their non-target forms. Their initial overreliance on A-quantification may be explained by event quantification being cognitively less demanding than entity quantification, and their non-target productions likely result from their developing grammatical systems. We argue that the acquisition of universal quantifiers involves multiple factors, such as cognitive complexity, children's developing grammatical systems, and input frequency, interacting with each other.