Surface electromyographic (sEMG) data impart valuable information concerning muscle function and neuromuscular diseases especially under human movement conditions. However, they are subject to trial-wise and subject-wise variations, which would pose challenges for investigators engaged in precisely estimating the onset of muscle activation. To this end, we posited two unsupervised statistical approaches- scree-plot elbow detection (SPE) heavily relying on the threshold choice and the more robust profile likelihood maximization (PLM) that obviates parameter tuning-for accurately detecting muscle activation onsets (MAOs). The performance of these algorithms was evaluated using the sEMG dataset provided in the article by Tenan et al. and the simulated sEMG created as explained therein. These sEMG signals are reported to have been collected from the biceps brachii and vastus lateralis of 18 participants while performing a biceps curl or knee extension, respectively. The acquired sEMG signals were first preconditioned with the Teager-Kaiser energy operator, and then, either supplied to the SPE or to the PLM or to a state-of-the-art algorithm. The mean and median errors, between the MAO time in milliseconds estimated by each of the algorithms and the gold standard onset time, were computed. The outcome of a PLM variant, namely, PLM-Laplacian, has been found to have good agreement with the gold standard, i.e., an absolute median error of 9 and 21 ms in the simulated and the actual sEMG data, respectively; whereas, the errors produced by the other algorithms are statistically significantly larger than that incurred by the PLM-Laplacian according to Wilcoxon rank-sum test. In addition, the advocated approach does not necessitate parameter settings, lending itself to be flexible and adaptable to any application, which is a unique advantage over several other methods. Research is underway to further validate this technique by imposing various experimental conditions.