As mentioned in a recent contribution*, cumulative gravitational potential of remote masses is about 108 times the sun's gravitational potential at our location. As potential gradients generated by remote masses due to large distance and isotropic distribution are negligible we won't be able to detect any sinificant linear static forces on a probing mass. This, however, shouldn't preclude other local phenomena like, in particular, those related to changes of spatial orientation. Centrifugal forces, Newton's bucket, Mach's principle, Sagnac's interferometer and Keith's rotational drag experiment** may be regarded as specific examples.
https://www.researchgate.net/post/Is_rest_mass_of_a_body_equivalent_to_local_accumulated_gravitational_potential_originating_from_remote_masses_of_the_universe