A surge of reduced capability and low-cost devices under the 5G framework for many Internet of Things (IoT) applications is foreseen. The new 3GPP standard, NR REDCAP, provides the means to develop such devices. However, keeping these inexpensive devices synchronized with the 5G network requires continuous synchronization algorithms running parallel with the receiver processing. Our analysis and literature agree that the acceleration of these algorithms on Single Instruction Multiple Data (SIMD) architectures is challenging because of the data dependencies in the recursive filter that is usually employed in synchronization algorithms and hence, requires a significant computing budget. The consequent need for activating extra hardware to perform continuous synchronization leads to rising device cost and higher power consumption which is undesirable. In this work, we address this problem by proposing an implementation that efficiently vectorizes the synchronization algorithm, including the recursive filter, on a wide SIMD vector DSP. The results show that the proposed implementation achieves a speedup of 9X over scalar processing. Subsequently, the synchronization kernel can run on a limited MHz budget of the vector DSP.