It has long been believed across languages that the "Agent-First" strategy, a comprehension heuristic that maps the first noun onto the agent role, is a general cognitive bias which applies automatically and faithfully to children's comprehension. The present study asks how this strategy interplays with such grammatical cues as the number of overt arguments and the presence of case-marking in Korean, an SOV language with case-marking by dedicated markers. To investigate whether and how these cues affect the operation of this strategy, we measure children's comprehension of a transitive construction (with scrambling and omission of sentential components) in a novel experimental setting where arguments and case markers were obscured to varying degrees through acoustic masking. We find that children do not demonstrate the agent-first interpretation strongly in the noun-verb pattern without case-marking, showing their uncertainty about the thematic role of the nominal when it is both the only argument in the sentence and lacks case-marking. They perform significantly better in the patterns with additional cues, the impact of which is asymmetric by age and by the nature of alignment between cues from word order and case-marking. These findings suggest that, for Korean-speaking children's comprehension of a transitive construction, the "Agent-First" strategy is activated properly only in conjunction with other types of interpretive cues.