Compact representation of multimedia signals using implicit neural representations (INRs) has advanced significantly over the past few years, and recent works address their applications to video. Existing studies on video INR have focused on network architecture design as all video information is contained within network parameters. Here, we propose a new paradigm in efficient INR for videos based on the idea of strong lottery ticket (SLT) hypothesis (Zhou et al., 2019), which demonstrates the possibility of finding an accurate subnetwork mask, called supermask, for a randomly initialized classification network without weight training. Specifically, we train multiple supermasks with a hierarchical structure for a randomly initialized image-wise video representation model without weight updates. Different from a previous approach employing hierarchical supermasks (Okoshi et al., 2022), a trainable scale parameter for each mask is used instead of multiplying by the same fixed scale for all levels. This simple modification widens the parameter search space to sufficiently explore various sparsity patterns, leading the proposed algorithm to find stronger subnetworks. Moreover, extensive experiments on popular UVG benchmark show that random subnetworks obtained from our framework achieve higher reconstruction and visual quality than fully trained models with similar encoding sizes. Our study is the first to demonstrate the existence of SLTs in video INR models and propose an efficient method for finding them.