is that the authors might see it like this:
The universe is infinitely old and infinitely large. However, the background spacetime geometry of this universe is a 3+1 dimensional de Sitter (dS) spacetime universe. That means 3 spatial dimensions and 1 cosmic time dimension (not to be confused with the 3+1 dimensions of our 'bubble' universe).
At a certain point in this dS geometry the universe comes to a point, this is the causal 'starting point' of eternal inflation. Extending from that 'starting point' are bubbles of universes that extend forward in time to infinity of cosmic time, and universes that extend backward in time to infinity of cosmic time. The bubble universes that exist going backward in cosmic time might move only move 'forward' in time from their perspective, but the bubble in terms of its location on the dS background spacetime is 'prior' to the 'starting point' of inflation.
So, there is no temporal origin to this universe. The universe doesn't start up one day, rather it always existed with an infinite past and infinite future. However, the 'starting point' doesn't actually get wiped away in the background dS universe, it stays 'there' just that it is not the first thing that happens in a temporal sense.
That at a single exact "moment", existence was not singularly forward and outward in direction, but that it expanded omni-dimensionally.
This is a correct interpretation, I think, except instead of omnidirectionally, it might be closer to accuracy to say bubble universes inflated bi-directionally with respect to cosmic time.
Suggestion that at the moment the beginning occured, it perfectly ("it" meaning the beginning) removed evidence of itself from existence.
Well, there are no initial conditions if this is what you mean. There are boundary conditions that remain. Part of the boundary conditions is that there is an area near the inflation 'starting point' where there are no immediate bubbles in that region. The bubbles expand in the past a little earlier in cosmic time from that point. Therefore, the 'starting point' remains, but since the model has infinite cosmic time to create an infinite past, the model should, I think, be considered an infinite past of universes along with an infinite future of universes as well.
I would encourage people to read the paper rather than rely on my interpretation. I might be way off and I'd hate to give the wrong or misleading interpretation.