Well, you live in an area with fairly good soil all around and enough rain water to keep everything composting, even without man's help. So, you can probably get away with this just fine.

Here, I would have to consider the difference in soil conditions. If I chose a foresty place, I would probably need to bring in a lot more materials for composting. And a lot of shit for fertilizer.

Tree leaves are toxic to many plants. That is why things don't grow in the shade, not because of the shade. But, it looks like you got lots of leaf litter, and can properly compost it. A composite pile, allowed to get to temperature will bake off all the toxins.

You may also like to look into food forests.
(Unfortunately, this means tearing out all the trees anyway)
With a food forest, you plant a canopy crop of good nitrogen creating trees. Then you plant smaller fruiting trees. And then you plant fruiting bushes and then you plant things that grow well in the undergrowth (like strawberries).

If you set these up correctly, they are a low work form of yearly food. You plant things like asparagus or artichokes, which keep growing up year after year.

But, but, you will still want raised beds for your tomatoes and chilis. Because, we can't have you going without salsa. That would just be bad.

So, you may want to look into hugelkultur where you take tree logs and then you pile dirt and compost stuff on top. And the logs break down providing nutrients to your garden growing above.