AFAIK, large particle interaction with the Higgs Field is not a thing. The Higgs field imparts mass to sub-atomic particles by tugging at them at Planck length scales, so electrons, gluons, quarks will interact with Higgs. Atoms/molecules/organisms are too large to directly interact with the Higgs field; the mass of those larger constructs is imparted by the force of the gluons holding them together.
There's a difference between being timeless, being time agnostic and causality (c). I think you mentioned Feynman diagrams in another post; those graphically show that interactions between sub-atomic particles are effectively equivalent interactions between their anti-matter pair, but reversing the direction of time (they are time agnostic, but still obey causality). In this way, any interaction between any 'things' (sub-atomic or macro scale) involves time in one way or another; back-to-front or reverse.
This PBS speaker (he is a physicist) has many videos on youtube; I think he's still the current host of the show; the show itself is pretty good IMO, they show concepts graphically for the most part, but get into the details and the math on occasion, and seeing things like the Lorentz transform presented graphically is pretty neat. His post on why time has a direction is pretty neat, among others.
I don't know if this gives any rationale that you were looking for, I might have got it wrong or not understood the question, but I think a more correct statement would have been that as long as a sub-atomic particle is interacting with others, it has to experience time in one way or another, but not necessarily in the same way that the aggregate of those sub-atomic particles (the 'thing') does.