Once I start thinking about space expansion and matter, I see a lot of issues that don't seem to be getting much attention.
For instance, the BBT postulates that "space" "inflated" and that separated matter by carrying it along with the space that it was in. However, matter can move through space under the influence of gravity and other forces (e.g. inertial reaction of force such as rocket propellant exhaust, photon reflection, etc.).
So, how does "space" interact with matter so that when it "moves" it moves matter? It does not seem to be a rigid connection. So, during BBT "Inflation", did matter lag behind "space" at all? And, in the vicinity of black holes, we say that matter "warps" space, but why does it not make space move continuously, flowing into the gravitational well. If matter sticks to space, and matter flows into gravitational wells, then why is it not dragging some space in with it?
There seem to be a lot of issues like that where theorists propose something to satisfy a problem in their desired theory, yet they seem to have no desire to consider the other consequences of their proposals beyond whatever they need to make their theory "work". In some cases, it seems that those other consequences might make their theory not work.
As for how matter sticks to space or "fields" in space, the Higgs Field seems to need properties that other fields do not have, such as "stickiness" to make matter have mass and behave the way we observe macroscopically.