Since the discovery of the Higgs boson in 2012 great progress has been made in precisely establishing its properties. Nonetheless, numerous questions remain open about the dynamics underlying the electroweak symmetry breaking of the SM, and therefore the nature of the Higgs boson itself. To shed light on this question, this project focuses on studying the Higgs boson's trilinear self-interactions, modeled by κ_λ. The experimental measurement of the Higgs boson's self-coupling strengths will verify the shape of the Higgs potential around its minimum and validate or reject associated theories beyond the Standard Model. While di-Higgs production has been the conventional channel to access κ_λ, this project explores an alternative process: The production of two same-sign W bosons and a Higgs boson via vector boson scattering (VBS ssWWh). This project presents the first detector-level study of VBS ssWWh in final states with the W bosons decaying leptonically and the Higgs boson decaying into b quarks, using the full simulation of the ATLAS detector corresponding to √s = 13 TeV and an integrated luminosity of 139 fb⁻¹. With this work, we demonstrated that studies performed by the theory community on the sensitivity of VBS ssWWh to κ_λ underestimated the background-to-signal ratio by a factor of 90. Using a first data-driven estimate on the background in the optimized signal region we perform a statistical analysis with the asymptotic formulae for significance computation with a one-bin histogram not including systematic uncertainties. The limits on κ_λ obtained in this study, κ_{λ , Run 2} ∈ [ − 121 , 121 ] , show that with this first cut-based signal region selection, the sensitivity of VBS ssWWh to the Higgs trilinear self-coupling is very low. A projection for the HL-LHC expectations of VBS ssWWh constraining κ_λ results in limits of κ_λ, HL−LHC ∈ [ − 54 , 54 ]. Although these results are outside the validity regime of the employed framework surrounding κ_λ , they should not be taken as a setback but rather as groundwork for the VBS VVH ATLAS analysis. Since VBS ssWWh is a very rare process, its observation will rely on innovative analysis techniques that will be explored in future work.