This question takes a lot of assumptions to answer properly. I'll give it a shot though.
(1) A wall can be approximated by two sideways ladders stacked on top of each other, lashed together with rope between 10-foot-poles.
Add up those costs and we get 1.25 gp / 10 ft, or 200 gp for 1600 feet.
Given the standard crafting rate of 5gp / day, a single person would, given all the raw materials, be able to craft this wall in 40 full workdays (40 feet per day).
5 people could finish it in 8 full workdays.
Personally, if these people are not trained carpenters, I would double that time.
But they don't start out with all the raw materials - they need to get those.
(2) Unfortunately, we don't have official stats for a tree - the closest I could find is a Treant - with AC16 + HP138.
A commoner proficient with a Handaxe would have a 35% chance to hit for 3.5 damage, which comes out to just about 11 minutes of constant chopping to fell one tree.
(3) Then we need rules for turning a tree into wall-sized chunks. Branches can use the small resilient wood object statistics (AC15, HP10) and would take a little over half a minute each. Around 20 branches adds another 10 minutes, bringing us up to a 21 minute total for one tree.
(4) A single solid trunk probably isn't very useful for wallbuilding, so cutting it again would be necessary: add on another 11-minute chopping session to cut it down to size.
(5) Observing the Treant picture in the Monster Manual looks like one tree could be used as the materials for 20 feet of wall - so we're looking at chopping down 80 trees for your full wall.
(6) A Short Rest between trees to regain strength brings us to ~1.5 hours per tree, or 5 trees per day. That's 16 days of 1 person collecting materials, or 4 days for 5 people (because you can't spend fractional downtime).
Using those 6 assumptions and adding all this together gives 12 days to create a wall from scratch if 5 commoners - proficient in carpentry - devote all of their time to doing so.
However, if you instead have two 9th level sorcerers, you can create a 1600 foot wall in 40 minutes simply by 4 casts each of Wall of Stone, making a permanent 200ft x 10ft x 3in wall each time.