Epoxy fillers are incredibly handy, as they let you ▶dial in the desired level of thickness at mixing time — ketchup consistency, mayonnaise consistency, or peanut butter consistency.
There are a wide variety of commercial epoxy fillers available to professionals. However, hobbyists often use at-home replacements, and any fine powder can work. Things I've heard suggested — baby powder / talc, flour, cornstarch, tapioca flour, the fine sawdust that's produced by an orbital sander, any solid that's dry and can be ▶processed by a coffee grinder, and graphite.
Products the professionals use[2] — fumed silica, microballoons / microspheres, and wood flour (which is sawdust that's been finely-ground).
Most epoxy fillers aren't transparent. Some ways to achieve transparent thickened epoxy:
Hollow glass spheres ('microspheres') are transparent. (I believe that microspheres provide limited thickening, and that they're used more often for bulking and for making the cured epoxy sandable. When a lot of thickening is desired, microspheres are often combined with a separate thickener. TODO: Try it, I believe they provide some thickening on their own.)
TODO: People who use acrylic paint have modeling paste that significantly thickens the paint. It's supposed to dry clear. One possible downside: Most of the mass of this is acrylic binder, and that binder might be weaker than epoxy, or of other epoxy fillers (that are usually solids).
Some epoxies are formulated to be high-viscosity without fillers, and some of these epoxies are clear. Some examples: [1][2][3][4]
Most of these are marketed to artists specifically, though they can be used for other things.
wait some time
Epoxy gradually firms up as it cures, and there's a period where it's becoming somewhat stiff but can still be shaped some. Each epoxy product has a different quoted work time. If the epoxy is significantly colder or warmer than normal, that will definitely adjust the work time as well.
Some epoxies, such as Apoxie Sculpt[2][3], specifically advertise this feature. (On that page, they refer to "cure stages", such as waiting 10 minutes, or waiting 20 minutes. Total work time is quoted as 1-3 hours.)
cooling
If you cool the two components before mixing them, it will definitely thicken the epoxy[2]. However, air bubbles will stay trapped in the resin more easily.
how to decrease viscosity
additives
Adding lacquer thinner or denatured alcohol to epoxy will thin it out. [1][2]
heating
Heating the two components before combining them also decreases the viscosity. However, I heard there's a limit, after which overheating decreases the working time significantly. (TODO — expand)