No idea if this would work, but:

https://www.amazon.com/Protective-Carrying-Speedlite-Digital-Hermitshell/dp/B01LYXN7RZ

One of the Q&A lists the dimensions as: 4" x 8.7" x 3.1"; and Godox lists the V1's dimensions as 3" x 7.8" x 3.7".

The Neewer TT560 is probably a rebranded Godox TT560.