Bones and Pottery. Later, composites and (natural) plastics
It depends slightly in what the Gods define as "trees".
A redwood is a tree. So is a majestic Oak. But what about a crabapple, at 6ft tall shrub-shaped? Or a dwarf willow, which is smaller than the average Twinkie snack?
Is Bamboo a tree? This is a very important question!!
Assume anything that generates what we would cal "wood" is a tree. Thus no trees, many larger shrubs are forbidden, bamboo is forbidden but reeds are not.
SO, no wood, and no metal.
What you have lost:
*Abundant cheap strong building material
*Abundant cheap tools
*Easy access to large fires. You still have easy access to small/campfires by using grass and dung.
*virtually all access to HOT fires
*the ability to shape and cut hard stone. This includes making blocks of hard stone, and mining in most rock. Shaping hard stone like granite is virtually impossible without access to hard metal tools. (much!)Softer rocks like limestone and sandstone can be shaped by abrasive methods, but they make very poor tools. And hard-rock tools would need to be ground down to shape using the most ridiculously labor and time intensive methods.
Pottery. And that fancy pottery called Porcelain. And that enormously fancy pottery called Glass.
You still have access to good clay, and the means to shape it.
Basic curing can be done with a grass fire.
Hard curing pottery will be problematic, grass and shrub and dung fires are simply not hot enough.
You could use bone for the fire, but the amount you would need to burn to fire pottery would be prohibitive. Figure 20kg of bone burnt to fire each 1kg of hot-fired pottery or porcelain or glass. You would run out of bone very quickly!
But what about charcoal? oops, that's made out of wood.
But what about Coal? Yes coal would work just fine. Unfortunately the amount of coal that can be accessed without using any metal tools is severely limited. On Earth the vast majority of open-air coal seams were completely depleted by the early middle ages, and that was by a culture that had access to wood and charcoal for fires!
Still. You can make household level tools and appliances out of roughly shaped rock and semi-fired pottery and bone.
Later, when you develop the technology, you will be making a LOT of your tools and materials out of composites. NO, not industrial era fibreglass and carbon fiber! But rather from bone and grass with somewhat natural glues. Pressure-molded grassfiber & shellac axles. Layered woven reed armor. Plastics made from pressure-treated insect Chitin. That sort of thing.
It would not be easy!
Edit 8 feb for OP question edit.
technology level would reach that of the medieval period before not having access to more wood or metal afterward
Instant, global catastrophe.
People would LOSE access to both metal and wood, which they have had since antiquity, which they have build their technology around, which 100% of their infrastructure is based upon.
Mass starvation and death would follow, and Human culture would regress to (early) stone age.
It's like being both blind and deaf. An enormous handicap, but if you grew up with it, you can possibly cope. Possibly.
But virtually no-one can cope with everyone losing all sight and hearing at the same time.
Nor could society cope with losing access to metal and wood in an instant.