Any kind of a temporary stick strong enough to hold the vine and not rot in the next 2 or 3 years should work. I’d try to dodge the grape roots … and pound it into the ground as close as possible to the grape trunk; fasten it near the top of the fence (with good twine or wire), then loosely tie the vine to the stake with flexible plastic tape. Gently tie 1 or 2 new ‘shoots’ from the highest point of the current vine so they may follow this stake to the top. With two, you can guide them in opposite directions across the fence… Leave most side ‘branches,’ you can prune them later, or use one if the uppermost branches don’t do as well.

Grapes grab with their tendrils, so don’t bother ‘wrapping’ it around the stake. Just have something for it to cling to when it reaches the top of the fence. This winter, study grape growth habits; they put out a lot of growth and (eventually) 80% of that ‘excess’ growth needs to be pruned away, yearly. If you don’t, they’ll become a thicket – weigh down the fence (or whatever support), shade their fruit and become very difficult to ‘unravel’ when you decide to…

I suggest ‘cane pruning’ when the times comes; keeps the load light and manageable …but we’ll deal with that after it reaches its current goal - Sunlight