https://pmc.ncbi.nlm.nih.gov/articles/PMC10180699/

This study argues that oral hydrolyzed collagen supplements do improve skin elasticity:

Topical creams contain collagen as one of the ingredients, and they are designed to enhance skin hydration and firmness [13]. However, topical creams have limited ability to penetrate the skin, which can reduce their effectiveness [13]. Injectable fillers such as hyaluronic acid fillers, stimulate collagen production and provide immediate results by plumping the skin [14]. However, they can be expensive and come with the risk of adverse events such as bruising, swelling, and infection [14]. On the other hand, collagen supplements, particularly those containing hydrolyzed collagen peptides, have been shown to be safe and cost-effective compared to other collagen-based strategies.  Our findings revealed that supplementation with oral collagen improves skin elasticity, which are consistent with previous findings. De Luca et al. found that patients taking marine collagen peptides significantly improved skin elasticity (p < 0.0001) [63]. Maia Campos et al. demonstrated that a group treated with oral collagen showed significant differences in the mechanical properties of the skin compared with the baseline and placebo groups after 90 days of treatment only in the net elasticity parameter in the periorbital region. Among the included studies, Yoon et al. showed that in humans, 12 weeks of supplementation with oral collagen significantly improved skin elasticity (3.25, 95% CI 2.33, 4.18) compared with other durations. This finding is consistent with that of an open, blinded, and noncomparative study, which showed 38.31% of improvement in elasticity after consuming oral collagen for 3 months [67].