Not true, at least according to theory. It is space-time itself that is expanding or accelerating. The objects (galaxies, etc), although moving further apart with time, are not actually moving *through* space but rather remaining where they are, outside of local gravitational movements/interactions.
“It is space-time itself that is expanding or accelerating.”
Sure, that’s fine, but I don’t think it solves the problem. There is still an acceleration to the expansion. Acceleration just doesn’t happen without some continuous application of force. If the big bang simply set spacetime to expanding, it would not be accelerating. Something must, right now, be continuously acting on spacetime to increase the velocity of the expansion. Not an event billions or trillions of years in the past.