Plasmonic metal nanoparticle (NP)–graphene (G) systems are of great interest due their potential role in applications as surface-enhanced spectroscopies, enhanced photodetection, and photocatalysis. Most of these studies have been performed using noble metal NPs of silver and gold. However, recent studies have demonstrated that the noble metal–graphene interaction leads to strong distortions of the graphene sheet. In order to overcome this issue, we propose the use of Ga NPs that, due to their weak interaction with graphene, do not produce any deformation of the graphene layers. Here, we analyze systems consisting of Ga NP/G/metal sandwich coupling structures, with the metal substrate being, specifically, copper (Cu) and nickel (Ni), i.e., Ga NP/G/Cu and Ga NPs/G/Ni. We experimentally show through real-time plasmonic spectroscopic ellipsometry and Raman spectroscopy measurements of the quenching of the Ga NP localized surface plasmon resonance (LSPR) depending on the wetting of the graphene by the Ga NPs and on the electron transfer through graphene. Theoretical finite-difference time-domain (FDTD) simulations supportively demonstrate that the LSPR in such sandwich structures strongly depends on the contact angle of the NP with graphene. Finally, we also provide evidence of the electron transfer from the Ga NPs into the graphene and into the metal substrate according to the work function alignments. These considerations about the contact angle and, consequently, geometry and wetting of the metal NPs on graphene, are useful to guide the design of those plasmonic systems to maximize electromagnetic enhancement.