Need help with the beginning of the game...

[ZedClampet]

I'm on one of the first quests--to attract 100 farmers--but it has stopped at 96. There are only a handful of things I can build, and I've built multiple of each. We have tons of fish, lumber, planks, etc. There is plenty of housing (I built two extra houses).

It doesn't appear that there is anything else I can do. I'm just waiting for 4 more farmers, but I sped up time to maximum for several minutes and didn't get anymore farmers.

[Gregomoto]

Maybe your farm houses are at max population.
Try to built one more farmers house.
The max population of farm houses is influenced by fulfilled needs.

[ElPrezCBF]

While having adequate warehouse inventory is important, having 100% market access to all current needs is just as important for full pop growth at current needs. The key word is "100%".

I think there are 2 possibilities. All houses within range of your market have 100% of their needs met (not necessary to meet all needs to get to the next pop tier but all needs must be met 100% for the current tier) and no houses have partial or completely absent market access. Which means you need to add new houses close enough to the market and connected to it by road such that they have 100% access to all current needs for further pop growth.

Or some houses only have partial market access, meaning if you look at their needs bars (click on houses furthest from the market to examine them), some are not full even after you've waited some time, i.e., mousing over those bars would show a message that their market access to that need is less than 100%. If so, either move them closer to the market and again connected by road such that all their current needs continue increasing to 100% or build another market near them to achieve the same effect. This should bring in additional pops.

[asterix52]

One trap you may be falling into is the way the house's maximum population is shown. For farmers, it will say x of a number up to 25, depending on which DLCs you have. However, many of these potential farmers need Lifestyle goods. In order to get the houses to be eligible for upgrade, you need to satisfy Marketplace, Fish, and Work Clothes to 100%, which will give you 10 population (in a farmer house). No matter how much spare Fish and Work Clothes you have, you can't get above 10 Farmers without Lifestyle Goods, which you won't be anywhere need having yet. So, you need to have at least 10 farmer houses and they must all have 100% Marketplace coverage.
The numbers of population you can get from fulfilling everything in the basic needs tab is 20 for workers, 30 for artisans, and 40 for Engineers.
I suggest you take a look at https://anno1800.fandom.com/wiki/Needs#Lists_of_needs

[ZedClampet]

So I had 12 houses, and I clicked on each one and checked the market/fish and they were all at 100 percent and listed as "perfect". I decided just to build 3 more houses anyway, and moments after connecting them with roads it hit 100 farmers. Thanks to everyone for their help.