If it was me, I’d wrap them in parafilm and stick them in a ziplock (no need to add a moist paper towel or anything) then put them in the fridge for a few months. They don’t necessarily need extra dormancy, but I’ve found mid to late January to be a good time to start cuttings so I’d rather store them in the fridge and deal with them later. Any earlier and they are kind of a pain to baby inside and make sure they get enough light to keep growth from getting too leggy, etc. They’ll really take off in the spring when you get them out in the sun, so starting early really doesn’t gain much.
I start a minimum of 30 cuttings each year and I do it similarly to @cdamarjian, except I use smaller tree pots (3x8 or 4x9) and just wrap the top 1/3 of the cutting with parafilm and put the other 2/3 of the cutting down into the soil, keeping it lightly moist. I get close to 100% takes as long as the cuttings aren’t too thin or in poor shape when I get them. They grow like this until late Spring or early summer when I move them up to 1 or even 3-gallon pots. There are a lot of other ways people start figs, but I find that putting them right into the pot they’ll stay in for at least 3 months is easier than moving them through different stages/pots and risking problems with each transition.
When you look at the bottom of the pots you can often see the roots before you see top growth.
And this was about a month after they were moved outside and they were ready to move up. You can see the roots have filled enough of the pot to hold the rootball together so they have very little or even no transplant shock.
