You must enclose the top if only to keep the chicks from flying OUT. It seems that they're the most aerodynamically adept at this young age. They must think they're really cool, having all those wing & tail feathers but little bulk, some of them can buzz around like little canaries.
I have some 3X3 pieces of parrot cages that I zip-tie together to make a big bottomless oblong. I enclose the top with orange plastic safety netting that is clothespinned to the wire sides. I'll put my chickies out in the yard enclosed in this during the day, and bring them in at nightfall.
In our So Fla climate, they can be outdoors at just a few weeks. I set them out when they get old enough to make an awfully poopy mess in their box.
I keep a box or nursery pot in the MIDDLE of their outdoor enclosure for them to run into for shelter or safety. Because our hawks are sometimes attracted to the sight of chicks outdoors and will land on the ground right outside their fence. I once lost a chick because it ran behind a box set right by the wire, thinking it was safe, and the hawk was able to peck it dead through the wire and was in the process of pulling out bites when I shooed him away.
There's a reason why the term "Mother Hen" has become synonymous with extremely protective parenting. There's a lot of things that enjoy a chick dinner, that's why chickens brood such big clutches. It gives them extras to spare.
The only way to keep your chicks 100% safe is to carry them around on cushions all day. The next best thing is to take every precaution you know of and learn from your mistakes & those of others.
I wish you & your chickies all the best.