Q.Can You Please Recommend A Climbing Vine To Cover A Trellis Relatively Quickly That Is Not Invasive In Ohio?
Flowering would be nice — especially in pink or purple — but I am more concerned about it growing quickly and it not taking over my garden beds.

Certified GKH Gardening Expert
Here are some options according to your zone. The clematis vines are not invasive that I know of EXCEPT the Sweet Autumn Clematis. It has small white blooms in the fall. It is frightfully invasive. Another to avoid that I see below is the trumpet vine, campsis radicans. That is one many have regretted planting.
I could recommend trumpet honeysuckle and crossvine, also. Trumpet honeysuckle, though not invasive, grows thick and heavy so you need to have a sturdy trellis or it will all come down in a storm. I speak from experience. I love the plant for the hummingbirds it brings. I have not planted crossvine, but I know others who have and they love it.
https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-5/hardy-vines-for-zone-5.htm
https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-6/zone-6-evergreen-vines.htm