What comes to mind is starting with a proper soffritto. With carrots, celery and zucchini you've already got a solid base, but the key is not treating them all the same: heat some oil in a pot, throw in finely chopped carrots and celery, and let them brown a bit for 3-4 minutes. Only after that add the zucchini and tomatoes. Meanwhile pour in water or broth (whatever you have), add a pinch of salt and spices if you want, and when it boils turn the heat down. In 15-20 minutes the soup is ready.
The real mistake everyone underestimates is throwing vegetables with different cooking times in together from the start. Tomatoes fall apart in two minutes, carrots need ten or more. If you cook them together you end up with mush on one side and raw carrots on the other. That's why the initial soffritto isn't just for flavor: it's about timing. By starting the harder vegetables first you give yourself a time advantage over what cooks faster.
If you also have onion, garlic, or even homemade stock cubes in the fridge, even better. But with what you've already mentioned you can make a decent soup. The important thing is not to rush in the final minutes - control the heat and wait, rather than trying to speed everything up together.