Context. The driving and excitation mechanisms of decay-less kink oscillations in coronal loops remain under active debate. The photospheric dynamics may provide the continuous energy supply required to sustain these oscillations. Aims. We aim to quantify and provide simple observational constraints on the photospheric driving of coronal loops in a few typical active region configurations: sunspot, plage, pores, and enhanced-network regions. We then aim to investigate the possible interplay between the photospheric driving and the properties of kink oscillations in the connected coronal loops. Methods. We analysed two unique datasets of the corona and photosphere taken at a high spatial and temporal resolution during the first coordinated observation campaign between Solar Orbiter and the Swedish 1-m Solar Telescope (SST). We applied a local correlation tracking method on the SST/CRISP data to quantify the photospheric motions at the base of coronal loops. The same loops were then analysed in the corona by exploiting data from the Extreme Ultraviolet Imager (EUI) on Solar Orbiter and by using a wavelet analysis to characterise the detected kink oscillations. Results. Each type of photospheric region shows varying dynamics but with an overall increase in strength going from pore to plage to enhanced-network to sunspot regions. Differences can also be seen in the amplitudes of the fundamental kink mode measured in the corresponding coronal loops. This suggests the photosphere is involved in the driving of coronal kink oscillations. However, the few samples available do not allow the excitation mechanism to be further established yet. Conclusions. Despite oscillating coronal loops being anchored in seemingly a statica strong magnetic field regions, as seen from coronal EUV observations, photospheric observations provide evidence for a continuous and significant driving at their base. The precise connection between photospheric driving and coronal kink oscillations remains to be further investigated. Upcoming coordinated observations between Solar Orbiter and ground-based telescopes will provide crucial additional observational constraints, with this pilot study serving as a baseline for future works. Finally, this study provides critical constraints on both the quasi-steady and broadband photospheric driving that can be tested in existing numerical models of coronal loops.