You can start your render range at some positive frame (or use negative frames) and keyframe a starting motion to your objects. The rigidbody sim will consider the object's current motion vector when it takes over the simulation.
I used this method here: https://youtu.be/f036R6d_DiQ?t=44
You can change the Rigid Body Cache settings under Scene Properties if ...
i am pretty sure it is because the messy geometry of your objects.
Here you can see:
and it should look like this:
the edges should be parallel.
your sensitivity is much too high:
Set it to 0.
set shape to mesh
apply scale + rotation
Hint: your objects have too much geometry. This is not necessary and just slow down the rigid body calculation.
One way is to use Deactivation:
You can keyframe the Deactivation box on at 0 and off at some other frame, and enable Start Deactivated, and the rigid body won't do anything until Deactivation turns off or until another rigid body collides with it.
Another way is to use a breakable constraint:
Here, the rigid body is anchored to another, animated rigid ...
This was written for those with reasonable experience...
The Blend file will be posted up if asked for but it won't help a lot because everything ends up baked & keyframed.
Vases don't actually bounce all that well so you don't really need physics in this case. Once at the floor, the solid vase is switched over to the cell fractured version, and that's ...
Two ways to do this:
Use collision collections to control collisions:
"Collections" here is kind of legacy; they're not like modern (2.8+) collections. Instead, by assigning a rigid body to one of the 20 collision collection layers in the rigid body settings, you tell Blender that the object should only undergo collisions with objects that exist ...
Since your pins have holes at the bottom, I think you should not use mesh shape, it may cause some intersections in physics, which tells blender to throw pin away. Change it to Convex Hull, and remove collision.
After that, I noted that pin doesn't throw away, but gently falls down.
I found that it is because it sits directly over the edge, so I moved it ...
Your lead pin does not have the same settings. It does not have rigid body physics; it has collision only (which doesn't interact with rigid body physics, by the way.) It has, in some way, acquired a cache that makes it move. Apparently, a few other pins have as well (pins with RB rather than collision.) Something is bugged, but it's hard to say what ...