Convergecast is a fundamental operation in wireless sensor networks (WSNs). To support long-term deployment of WSNs, sensor nodes normally operate at low-duty-cycles. However, the low-duty-cycle operation significantly reduces the communication chance between nodes. Consequently, the risk of data collisions significantly increases when multiple senders transmit packets to a receiver during its very short active period. This problem further causes not only wasted packet retransmissions, but also a large delivery latency. Under such conditions, collision-free medium access is more appealing than recovering after collision for low-duty-cycle WSNs. In this work, we propose an <u>i</u>ncast-<u>co</u>llision-f<u>re</u>e convergecast protocol, named iCore, to address the many-to-one collision problem in low-duty-cycle WSNs. iCore employs the dynamic forwarding technique, establishes a non-conflicting schedule for efficient convergecast, and improves the channel utilization by allowing senders to opportunistically transmit packets once detecting unused slots. Specifically, we design efficient forwarder assignment and forwarding optimization algorithms that ensure low end-to-end latency under diverse data traffic types. Through comprehensive performance evaluations, we demonstrate that, compared with the baseline protocol, iCore effectively minimizes the end-to-end delay by 25% ~ 57% and maintains high delivery ratio and energy efficiency for different many-to-one convergecast scenarios.