Asklemmy

Well, there's the guerrilla option, but it's significantly more difficult with trees than it is with flowers or smaller plants.

Best is if you can find native species that are threatened with extinction or some kind of tree that is beneficial to threatened native insects or birds that enjoy a protected status. Any protected status could help keep the project alive even if it was not sanctioned, but it's still a struggle to do guerrilla style.

Do some research about the types of trees that will easily grow in your environment without any/much watering or fertilizing beyond getting them established, which can be anywhere from one to five years depending on how harsh the climate is and how tough the tree is.

And for acceptance from the city, go for fruitless varieties. They will typically balk at anything that produces fruit because it attracts rodents and will require maintenance. Also avoid trees that sucker easily or sprout prolifically from seed, especially if they're going near sidewalks.

Also do the research on how much asphalt, cement, sidewalks, parking lots, etc. contribute to increasing temperatures and the difference when they're shaded by trees. It's a substantial difference.

If you can present a plan to whoever is in charge near you that offers them a way to win points on the environmental arguments without adding any type of city workload or responsibility, you might just be able to pull it off with their blessing or even some financial support. You can try framing it as a community project or community outreach project. Try to get the trees discounted or donated by local nurseries in exchange for some kind of advertising. Get the planning and planting done by volunteers. It's a win-win for everyone.

Alternatively, you can get a bicycle or even an e-bike. The higher efficiency and speed means you're using less energy and staying cooler doing it. And as a bonus you can explore more widely, covering more ground in the same amount of time, and even use it for transporting things from the store or going to work.

Best of luck to you!

Edited to add: Make sure the planting is at least done under the guidance of someone who knows how to plant trees. It is actually quite easy to fuck that up and ruin the trees prospect for survival.