Helio, I think the analogy is fitting.
But, the problem with the BBT is that it is an extrapolation based on everything going back to a single point. Claiming to stop short of that point by 10^-x inches does not alleviate the issue of why would it even get that small. Unless there is some basis for a beginning, there is a remaining question about whether the BBT extrapolates too far back in time, and whether there are some other phenomena that we are missing that makes for a "bounce" or some other process not headed inexorably to an infinitesimal. The BBT cannot logically escape the infinitesimal just by refusing to talk about it.
Regarding space "inflating", "expanding" and "warping", it always amuses me that the people who believe that it does those things will also adamantly refuse to consider that space might also "flow". Yet, one explanation of why light cannot get past an event horizon to get out of a black hole likens it to a speedboat trying to go up-river in a waterfall that is going down-river faster than the speedboat can travel. But, when somebody tries to point that out to BBT advocates, they respond with "that is just a lie we tell children". Insulting form of deflection!
Actually, if you look at it objectively, the escape velocity from a mass correlates exactly with the time dilation in proximity to that mass. And, the Special Relativity time dilation also is the same as would be calculated for an observer standing on the surface of the mass with space flowing by going into the mass at the local escape velocity, when compared to the time seen by another observer at infinite distance from the mass, where the velocity of space into the mass would be zero. In other words, it is the same as the Special Relativity time dilation between 2 observers traveling at different velocities "through space".
I think that is interesting, but BBT proponents just don't want to discuss it.
And, I think it would be useful to conduct an experiment to see if the time dilation still correlates with the escape velocity as a function of depth below the surface of a mass. Or, does it correlate with the local gravitational force, instead, which goes to zero in the center of the mass. That would be of direct interest with respect to the observations we have of star orbit velocities inside the mass of galaxies. But, the replies I get are that we already know the answer from the theory, so why bother doing the experiment. Obviously, you do that type of experiment to test the theory. Unwillingness to even consider it is a sure sign of non-scientific thinking.
One of the big problems with current cosmology is that practitioners are clinging to the concept that the universe is basically uniform in all directions, always has been and always will be. And that persists, even with some evidence to the contrary. The main reason it persists is that to think otherwise opens so many possibilities that it would be extremely difficult to make sense of it. And, space "flowing" could do just that.
Remember, I am not claiming to "know" that space "flows". I am only asking how we know that it cannot flow.