Edit: I just noticed you prefer non-psi. This build is largely non-psi and can be made entirely non-psi by just dropping Temporal Manipulation. But the small investment in psi will help greatly against the 2-3 late game enemy types that are rarely encountered but otherwise fairly difficult to fight with throwing weapons.
Crafted grenades are among the highest damaging attacks in the game through the first two acts. And being AoE, it makes throwing builds a breeze in the early game. Other builds will out scale throwing in terms of single target damage. But throwing will always be among the best at killing multiple medium to soft targets, which make up a lot of the most difficult fights. And throwing can still comfortable deal with hard, single targets through poisons, disables, and some supplementary psi. Overall, throwing builds have made for my easiest Dominating playthroughs. Here's an example build assuming you have Expedition:
Level 1:
http://underrail.info.tm/build/?AQMKBgUDBQgADwAAAAAPAAAABw8PDwAIAAAADwAADysnL9-_
- Throwing builds carry a lot of weight, but would like to spend attribute points elsewhere than strength. So Pack Rathound is good.
- The other starting feat can be anything, but I do prefer Quick Pockets.
- Your crafted grenades are much stronger than what you can buy, so Chemistry is very important.
- The hard part of the early game will be the first three missions when you're struggling to afford your grenade components. Once you have an income, this build becomes super strong and straightforward.
Level 10:
http://underrail.info.tm/build/?CgMMBgUDBQgAPAABAAA8AAAABw88PBgIAAAAPAAAPCsnL2EWKlE-378
- 65 skill points are not spent. Distribute as you'd like.
- Continue leveling Temporal Manipulation as a means to kill especially hard targets.
- At this point, you have your most important feats (Grenadier, Three-Pointer and Fatal Throw).
- Sure Step is optional but let's you throw
Level 16:
http://underrail.info.tm/build/?EAMOBgUDBQgAWgAAAABaAAAABw9aWi8IAAAAWgAATysnL2EWKlE-wojCh1zipbwB378
- 114 skill points are not spent. Distribute as you'd like.
- This isn't completely optimized, meaning some of the skills are a little higher than needed, since for your first playthrough you won't know all the ways to temporarily boost your skills.
level 17-30: no link, you can pretty much build off level 16 however you want, but...
- Tranquility is very recommended to boost your output of Temporal Distortions, which combined with Stasis is your best way to kill ultra tough single targets (esp. robots which are immune to poison/heat).
- Specialize fully in Three-Pointer (it's insanely good). Remaining specialization points can go into Fatal Throw health threshold, Future Orientation, or something else of your choice.
- For Veteran Feats, I recommend Expert Throwing, Increased Dexterity, and Advanced Psi Empathy or Empowered Temporal Manipulation.