Probably better if you can attach your simplified blend with issue. Use https://blend-exchange.giantcowfilms.com and paste given code into your question. This topic is quite case sensitive :) and not always there is a solution.
Here with Cubes
- Collisions > Shape > Box
- Surface Response > Friction > 1 (Bounciness > 0)
(probably also for small Cubes > Dynamics > Damping Translation > 0)
Important - Apply Scale Ctrl+A to all objects.
Edit according to the given file:
- You didn't set Collision Shape to Box.
- Also one very important aspect is set Geometry to Origin for proper simulation. If collision box doesn't fit to your high-poly mesh, move vertices a bit closer to border in edit mode.
Sidenote - Is it OK to have object dimension just 4 mm? On my computer it starts flicker that can be fixed in 3Dview's side panel (N) > View Clip Start = 1 mm End = 100 mm.
I'm asking because part of problems can be a size. Simulation on these micro values is not too much stable in general. But here works without bouncing with RB Active object > Mass = 0.0001 mg and RB Passive object with Strength = -10000.