I’m not sure if anyone has ever been able to do a proper estimate, but it is easy for me to think that the world-wide population could have been much larger than most people might imagine.
Moreover, the “bottleneck” population estimates are made on the basis of a genomic analysis and hence only estimates the size of the population that contributed to the majority modern human genome.
There is, I think good reason to believe that some fairly significant populations of pre-Toba humans could have survived to the east of the Toba caldera, in Java, the lesser Sunda Islands, and what is now New Guinea, as well as in some parts of penninsular Malaysia.
These stocks may be the ancestors of the negroid peoples of New Guinea and the Andaman Islands. These groups have not made any significant contribution to the wider gene pool, and would have been immaterial to the bottleneck. They may have survived in much larger numbers than the majority ancestors, only to dwindle later under pressure from modern humans in the last 15-20 thousand years.
Perhaps some hominid variants such as the “hobbit” people of Sumba who apparently co-existed with pygmie elephants right up to the arrival of modern humans a few thousand years ago were survivors of the Toba event.
I think the article said they did their extrapolations from only 2 genomes. I am sure there are a number of genomes of isolated populations that could indicate a much larger population—the Saami of Finland, the Basques, the bushmen and pygmies, Esquimos, New Guinians, etc. Also, the south east Asian areas, especially islands would have been much larger, given that the water level was several hundred feet lower than today.
Regarding the Hobbits, I recently read an article saying that they were 700,000 years old. Of course in the past 100,000 years until they died out, their island would have been much larger because of sea level.
I recently read an article in Archeology Magazine about finding remains in India that dated to right after Toba. I might be able to locate it and add some information if you are interested.