Minecraft wiki entry for Survival_in_an_infinite_desert, associated text: You may be able to find dirt/grass, water, flowers, rabbits, maybe even seeds. If only you had any tools (a hoe or a pick even)!
You can try to get planks or logs from a Pillager Outpost or Mineshaft - but be prepared to fight. The absolute priority is 4 planks to make a crafting table. A bonus is 3 more for a wooden pickaxe.
If you find a living tree (in the river biomes of Buffet customized desert worlds only, and rare) or saplings in a village, it's "desert challenge over" and you can now transition to a normal, wood-based game of Minecraft.
However, on Superflat worlds with no structures, you are stuck as a pre-stone-age hunter-gatherer forever. You eat dead people, and your only tools or weapons are scavenged from dead people who never drop what you really need - four lousy planks, or failing that, a pickaxe and a hoe - the legendary tools of the gods. So, there is no way to ever progress beyond that. Just a grim evolutionary dead end.