I actually suggested one of the current HOF Challenges involving a later era start culture victory that might involve alternatives like Corporations. However, I suggested a Ren start which turned out not to be too early to really involve corps much, although you could, for Culture VC as normal methods were still quite suitable. So it would need to be Industrial at least.
Another option, which avoids a later era start like Industrial and all its trappings, is to have a normal Ancient era start. However, place possible limitations like the following to encourage later era Culture win.
1) Must not found any religions. It's fine to adopt and spread religions that spread to you, but not be first to any religion founding tech.
2) We can build Temples and Monasteries as we choose for happy and research boost, but can never build a Cathedral or the like of any religion. Hermitage and later era culture boosters like Broadcast Towers are fine.
3) Cannot adopt Free Speech until you found at least one corporation.
4) Likewise, you can't produce a Great Artist until one corporation has been founded. (Free GA from Music is fine)
5) Additionally, we can never raise the culture slider until the second corporation has been founded.
6) We can spice things up by adding requirements like "must have at least 3 vassals at victory"
We can give something like this more thought, but basically Cathedrals/Free Speech/Great Artist Spam/Culture Slider are the big keys to early culture wins. Limiting or eliminating some of those factors should push a Culture Victory well into Corp range with much culture needed still for 3 L cities. We could go hardcore and eliminate/reduce some of those factors as we see fit or how we really want this game to run. Or just place all the parameters on a 2 or 3 corporation requirement.