Imagine everything man-made suddenly disappears but not the knowledge individuals carry. How long until we have an iPhone (or a plastic shirt button)? Would it even be any faster than the first time around?
We might lose electricity for a while. There's not a lot of utility for electricity in pre-industrial society. Like, given enough copper, I could make a wind turbine, but I can't casually make a useful lightbulb. Maybe a ceiling fan, but it would almost certainly be easier to run that off of mechanical power directly via a series of gears and belts. Electrochemistry would be a neat party trick, but I don't think my shoddily built wind turbine would generate enough juice to process aluminum.
Firearms would probably continue to exist. I could make a musket, and its utility for hunting and defense would make it immediately worth it. Black powder's not terribly difficult to manufacture from base ingredients.
Are we including domesticated crops as "man-made"? Because that would complicate matters. A lot of knowledge could be lost in the time it takes to rebreed the kinds of grains that allow for stable settlement.
We wouldn't need to re-invent writing, since that's just knowledge, and that would give a pretty big leg up in not losing a bunch of knowledge every time someone dies.
On the whole, if we keep selectively bred crops, I'd say we'd be bumped back to about the Middle Ages at the most. If we're losing the crops, then it would come down to whether we could preserve our more advanced knowledge long enough for agriculture to redevelop.
Seems pretty optimistic based on the Primitive Technology videos.
Respectfully, this is laughable given the constraints.
Without having access to the advanced techniques, I think it's unlikely we'd even reach the industrial revolution again.
All of the post-apocalypse LARP scenarios other responses are describing tend to assume at least books and some small number of durable structures survive. If nothing at all makes it, the first thing that happens is most everyone not living on a ground floor dies instantly from falling. Everyone living where it freezes dies in a few hours from exposure. Most people living anywhere experiencing a heat wave die from heat exhaustion in the next day or two. Most everyone else everywhere else dies from starvation or disease in the next few weeks. Even if you're living on a farm, you've got no fences or tools, so you better hope it's a farm with lots of edible plants and it's near harvest season. If you live in a city, you have no hope at all. Even existing food stores will spoil quickly with no containers or refrigeration. The people who do the best will be Hadza and uncontacted tribes and what not that lose their spears and tents, but all they have to do to get back to their prior situation is make more spears and tents, which thankfully doesn't require a global transportation network or modern manufacturing techniques. They're not the ones who know how to build iPhones, though. I'm not sure anyone knows how to build an iPhone, really. The knowledge is probably largely digital. The chief engineer at Apple knows where to look and who to ask, but no single person has all of the knowledge in their own head.
I am not really trying to get to anything except to have fun thinking about how society would organise itself. And since this is not an exam, everyone's free to think through different versions and enjoy the question as they like.
As for me, normally it comes up in a discussion and we develop and make assumptions as we go, but I've prefer to change as little as possible e.g. buildings/infrastructure do disappear but people "land" gently. And then most of what you said would be true: people in inappropriate climates, far away from a source of water or food die. I don't think it makes the thought experiment any less interesting to think about. In fact, the reason I like it is because progress may become so slow that some generations later we'd start believing or question in mythical iPhones and technologies.