For safety, I would be hesitant to recommend anything other than a permanent solution.
I would suggest a solid piece of 140 x 19mm KD Select Grade Merbau Decking - Linear Metre fixed in place with Buildex 8-18 x 30mm Climacoat Countersunk Ribbed Head Metal Tek Screws to the upright posts of the fencing. - MitchellMc
A strip of merbau decking would provide a more secure barrier. I'd also give it a couple of coats of Weathershield paint to match the colour of the railing so it blends in and less noticeable to the eye. - Walzz
We got a puppy 3 months ago and were faced with the same problem. First attempt was to get some leftover curtain material and tape it to the glass and floor. It didn't work, as the dog kept biting the material and tape. In addition, we get heaps of wind on our balcony and it kept rip the material right off the tape.
We got a pet playpen pretty soon after, and blocked off that part of the balcony with it. It worked quite well. Our dog is too big to fit under the gaps in the balcony now, so we use the playpen whenever we take our dot to a friend or family member's house. - knockhead
I would get some perspex and cut it to a nice thin section and attach it via some L brackets. Do it to the inside. Or you could do the outside also if you are confident. Acrylic perspex can be cut using a circular saw. The cut end can then be sanded smooth and even buffed up to a polished finish if desired. - BenjaminTaylor
Sometimes strata restricts what you can do structurally/cosmetically. I was thinking of simple plywood sheets placed against the metal. Maybe a tad of silicone to hold it in place, which should be easy to remove once your puppy has learnt the dangers of gravity. - Noyade
Baby gate panels. No drilling required and you can use them anywhere around the home. Adjustable screws that press against the wall. Worked a treat for us. Same as baby play pen. - Carol_Prime
I got the panels and have secured the balcony opening and our puppy can now go outside safely. I used a combination of ideas. Rather than screws, I used cables ties as there is small openings between the glass and the metal frame. - Martin2020
For those looking to do something similar, I suggest placing the Merbau panel at the bottom of the balcony railing. The cable ties go through the gap between the glass and steel post and past the steel horizontal bar. They then go back down at the bottom of the Merbau panel and then lock at the top.
You can use multiple cable ties for a more secure fit. However, if you want to fix it in a more permanent fashion you can use Zenith 10G x 30mm Galvanised Wafer Head Metal Screws. Please make sure to drill pilot holes in the Merbau panel for easier mounting to the steel.
I've placed images below to give you an idea of where to secure the panel. - EricL