Gunpowder weapons? Assuming it’s a high priority, ideally under a month (wood cannons wouldn’t be good weapons, but they’d be better than nothing), IF a good source of, say, natural potassium nitrate and sulfur is immediately available and known.
It could take a year or several, allowing time to locate, harvest, extract and purify nitrate; and local conditions (drier is better for extraction and preparation, since your scenario suggests ample water for survival) – dnd your luck with finding local base materials [ceramics, glass or metal] to make useful tools/adjuncts to the process. That’d be the first vaguely cannon-capable batch. I’d expect the quality to improve over the following years
Metal smelting can be done in earthen pit furnaces. The first usable samples could be done in weeks, given a suitable nearby ore, but it would take quite a bit of time, development and substantial use of local wood -> charcoal before it could be produced in significant amounts, and I wouldn’t take an ample local wood supply for granted if I had to depend my perimeter
Similar concerns and issues arise with glass and ceramics, though you should be able to get crude clay pots in weeks, assuming the season is suitable.
I’ve made both gunpowder and metal from ore in small amounts, for the heck of it, but I’ve never prospected for ore or synthesized suitable nitrates from nature. I’ve extracted and synthesized other nitrates, but not sodium or potassium, though I understand potassium nitrate can be (and was) extracted from natural guano, and have some idea of the chemistry to extract it, I have no idea how many of the intermediates would be independent challenges
Potassium hydroxide [once known as caustic potash] is easily produced by boiling wood ash. This or sodium hydroxide (lye from burned seaweed) was then boiled with rendered fats to produce homemade soaps well into the 20th century. It should be good enough to be a base material for crude potassium nitrate extraction or synthesis. As far as my limited knowledge goes, Sulfur would have to be mined to acquire sufficient quantities with suitable effort.
The real limiting factor to many advances would be immediately available local materials.
For example, many early cultures were able to purify (often by heat and beat) meteoric or bog iron, but couldn’t or didn’t smelt it. They may have made a few iron artifacts, but not many. We could shortcut a lot of development time by with simple undergraduate chemistry and geology knowledge of magnetism, smelting, copper, tin (hence bronze) and their ores etc. but ultimately I would be surprised if it took years to develop the skills to prospect and assess surface ores. I don’t think a substantial body of people still have those skills today.
– but what’s a few years, really? Realistically, it would be hard for me to assure too much in under a year (except survival basics) because nature has her own schedule. You won’t be able to effectively prospect for ore under thick snow; you may have to wait for dry or warm weather to tan leather; You’ll only have fairly green wood at first (it can take years to dry by storage) etc.
Here’s how I see the relevant classes of technology, but where a given technology falls on this scale may be heavily location-dependent
“Class 0” would be woodcraft and other basic survival skills – which would include a LOT of things, if you want to feed, clothe and shelter your ample supply of grunts through the winter (assuming your winters are anything like ours) The population of your community is a huge liability that human communities didn’t have historically. You’d almost inevitably die down to whatever level you can sustain, though our knowledge of hygiene would help a lot.
“Class I” would be mostly resource limited, because basic science would suffice, and should be achievable in a year, maybe two, in demonstration quantities, if local resources are found. If you don’t have a decent local source of (probably mined) sulfur, you can forget gunpowder; without iron ore, you might only find enough iron for compasses or iron-harvesting magnets (there’s reasonably pure iron dust on the ground all around us, but even with very good magnets, it would take a lot of time and manpower to gather an axe-worth)
“Class II” would require redevelopment of basic skills and might be resource-dependent as well. This could take up to a decade to be produced in useful qualities or properties. You can learn to “flint knap” in weeks, if you have sufficient local flint, but it takes years to be good. You can produce crude clay ceramics in weeks, but your products would continue to improve for many years or even decades, as you experiment with techniques and local materials.
Class III? That might be “requires infrastructure” – e.g. a water-driven mill for flour. Without metal, this could be built with wood-peg technology, but it’d take time to develop the needed tools and skills, Ultimately, that project may not be suitable until metals are available, because you have better ways to use your time (and develop the needed skills/resources)
Class IV might be “fit and finish” – using tools and materials to make better tools and materials. I guess that’s a sort of infrastructure and skill problem, but I perceive it differently, because a knowledge of historical techniques might not help that much with gruntwork infrastructure like digging canals or felling trees without adequate metal, but it could help you zip to the Enlightenment or even the late Victorian era in a single human lifetime