Why do you saute onion first?

A few things to consider. First, I seldom put garlic and onion in at the same time, because garlic burns much quicker. As for onions, they contain a lot of moisture/water, and because water will not go higher than the rather low temperature of boiling (211 or so, except under pressure cooking), it is helpful in many recipes to eliminate most of the water through evaporation, so that the pan temperature can go into a more optimal range for subsequent ingredients. I typically add garlic after much of the onion phase has been done.

Of course, zucchini has a ton of water, too, so a second factor about onions concerns how their sweetness emerges with varying degrees of browning (unlike zucchini, so far as I know). It's really important in certain Indian dishes, for example, to make sure you give ample time to softening and browning the onions in order for the hot/sweet balance to be where it should be.

Shriveled onion can be a great thing, so long as you're short of blackened.

If your onions are scorching or shriveling, your heat is too high and/or your pan is too thin.
1. Preheat the pan, slowly, over medium (NOT HIGH) heat until it is very hot, add oil, add the onions. That will immediately start to break down the onions, as it drops the temp. You will NOT get the desired result if you start and continue on lower heat.
2. Lower the dial to anywhere from med-low to low, depending on your pan and stove. "Sweat" the onions. This means you are slowly cooking the water out of them as they become translucent and golden. You can hasten the process by salting the onion, if you wish. Don't add garlic until the onion has started to soften and the pan is no longer as hot as when you began. Once the onion is golden and soft, if it isn't browning, increase the heat and keep stirring until it colors. If it looks like the onion is browning too fast, lower the heat, toss a couple of ounces of water into the pan, and stir. This will dissolve the brown bits (fond) evenly and once the water is cooked off, you'll be back in control.
3. Your onion and garlic should be almost completely cooked before you add the zucchini. Increase the heat as soon as you do, because the zucchini will exude a lot of water. As this water cooks off, the temp of the pan will be around 212F, so the onion/garlic won't burn, but you need to stir as soon as the underside of the zucchini browns, to cook all sides evenly.

Starting with the onion and garlic releases lots of caramelized compounds into the cooking oil/liquid, which will contribute complex, rich flavor to the rest of the ingredients.

Every beginning cook has the problem you are experiencing. You need to learn the required times and heat for your particular equipment, and that comes with trial-and-error. Eventually, you'll be in synch with your appliances and utensils!