There was no Toba bottleneck, more recent searching for verification of the *hypothesis* turned up evidence that was clearly not true.
The Mediterranean last dried up almost 6 million years ago, then refilled over 5 million years ago, in the Zanclean Flood. Subsequent drops in sealevel occurred worldwide due to glaciation, but by that time humans had been using watercraft for 100s of 1000s of years.
I decided to do further research on sea depths between Tunisia and Sicily and found the link below. It should appeal to your interest in sunken civilizations if you did not know this one before. Also the map shows that at the lowest water level, the distance between Tunisia and Sicily was only about 30 miles, and if you went from the island near Tunisia, only 22 to 24 miles.