Einstein did not think so, I cannot think of any reference of anyone who thought so, regardless of the Big Bang model.
Einstein had no involvement in Big Bang Theory when he published his Theory of Relativity. Most of his adult life, including his time spent at the Patent Office, and during his time as a Professor in Germany prior to publishing relativity show no hint, no sign whatsoever that he ever submitted any paper suggesting anything close to what you are suggesting.
You just threw the name "Einstein" out there in ignorance, thinking it would give your claim a sound of legitimacy.
You must define what the difference is between the Whole Universe and the Observable Universe.
But this is not what we observe. What we observe is that there are galaxies receding faster than light.
Matter cannot move faster than light.
But Spacetime itself can, because it is it's own properties that limit matter to less than "c," spacetime itself is not limited. The cumulative effect of expansion between us and a galaxy, say 14 billion light years distant, adds up to a speed greater than 300,000 km/s. If the Universe was static, this could not happen.
I believe that challenging the current models is a good thing. But it is logical you must fully understand the current models to really challenge them.
I do not agree with your logic, but I like that you debate it.