This is an extension of, or complement to, L.Dutch's answer, which was first. I upvoted it. So should you.
I'm fond of reminding people that 99.99% of the technology we enjoy today was invented in the last 150 years. Based on that observation, one could jump to the conclusion that what you're asking is possible, perhaps even plausible.
But that would be a lie.
150 years ago was 1870. Take just a moment to consider just how much infrastructure existed world-wide in 1870.
Assumption #1: A "single lifetime" is an 85-year period, from the day our teens are theoretically useful 15-year-olds to their deaths at an average age of 100.
Assumption #2: We'll assume that the available humans are capable of working and thinking like 30-year-olds from age 15 all the way to age 100. This ain't true. Humans on average don't really become industrially productive until around age 25 (physical and mental maturity) and start winding down physically at 45 and mentally at age 65 (these are rough and optimistic averages, of course). But even assuming you could get all 85 years out of your team — my answer still stands.
Infrastructure is, quite simply, the problem
Building any (and ONLY) one of the millions (not thousands, not hundreds-of-thousands, but millions) of components needed to successfully launch a crewed spacecraft equal only to Apollo 11 requires an industrial and technological pyramid of interconnected disciplines so vast that it's simply impossible for teenagers, no matter how smart or how unified, to complete in a single lifetime starting with (did I understand this correctly?) absolutely nothing.
Assumption #3: When you mean "no infrastructure," I assume you mean absolutely nothing. There are no utilities, no factories, no houses, no farms, no ditches... nothing. If I'm wrong with this supposition then you need to produce a SUBSTANTIAL AND HIGHLY DETAILED starting point for your humans.
Let's pick just one item: a single LS7400 NAND microchip, invented in 1966.1 That one object, the LS7400 NAND chip, required:
- A silicon foundry capable of at least 100µ geometries.
- A packaging and assembly facility.
- A testing facility.
Those three facilities, which can be combined under one somewhat large roof, require...
- Electron beams
- Photo lithography
- Robotics (crude compared to today, but nonetheless...)
And a bazillion other things. I know you're not an electrical engineer, but that industrial and technology tree just became ENORMOUS... and we're only at the first level of very basic dependencies. Let's jump near the bottom of that tree (not the bottom, just near the bottom)...
- Vacuum tech
All of which requires agriculture, mining, and logging, which requires more machinery, more tools, more factories, more industry.... Somewhere in that massive tree of dependencies are the industries that create hammers, screwdrivers, forklifts, cranes, furnaces (very precise furnaces, not just smelting).
If I tried to make this list comprehensive, I would literally (LITERALLY) write a book-sized treatise and the one and only thing I would have done is list the dependencies... I'd have actually explained nothing. A book.
- Animal husbandry (and you'll have to catch and train the horses... a LOT of them...)
And, of course, the millions (yes, millions!) of teenagers would need...
- Health care
- Homes (with household goods...)
Assuming most of them didn't die before developing the ability to grow, package, and distribute food to so large a group. And what did we get for that? One component out of millions, an LS7400 NAND chip.
But, let's say that our intrepid teens number in the tens of millions and are, somehow and magically, already organized into teams of tens, fifties, hundreds, and thousands, such that each group knows exactly what they need to do each step of the way. What then?
Assumption #4: They're humans, meaning their memories aren't perfect.
Which is important because without infrastructure, there would be no books, no guides, nothing but their memories to guide them until they could create books...
I can't take it anymore. Just the task of developing the infrastructure from scratch needed to record the knowledge they have so they don't forget it might take more than a lifetime. You can't have just one copy of anything, so now you're inventing movable type, printing, binding, paper, glue, thread, machines, tools....
I'm sorry, and I beg you to forgive me, but you're asking a question from an entirely untrained perspective.
What you're suggesting is impossible.
1 I designed 74BCT and 74ABT BiCMOS chips, which you'll find briefly described in that Wiki document, and the more complex MultiByte family of components based on that technology created by Signetics Corp, and then Philips Semiconductors. Geez, that was a long time ago. Feels like yesterday.