I have a cylinder below and on the top a sphere. I want the sphere should align on the cylinder so that the sphere below part goes inside the cylinder.
align.blend (1.1 MB)
Dimensions are a bit off in the original for any type of snapping, and there isn’t a dimension to the center of the sphere so have to do it the hard way…
Select the cylinder…
Add a loopcut and scroll for 2 cuts set it with the Left click…
select lower loop cut and then cursor to selected…
Set origin to cursor…
Select Sphere, then select the lowest vertex
Origin to cursor
then select cylinder…
cursor to selected
then select sphere
Object to selected…
that should get you really close to the right place…
You will then just have to Grab > Z and bring down the sphere till the outer edges match the cylinder…
I then did a Boolean Union and you have what you needed…
align-002.blend (1.0 MB) Blender 3.5 file…
You forced the center of the sphere 
ts.blend (995 KB)
Lower the sphere to the desired position of the cylinder,
Move the top polygon of the cylinder below to the center of the sphere.
If you do this, it’s about 0.49857, and if you center the sphere at 0.5, you’ll get it right.
It’s a little forced size, but… 
※ Dimensions used are metric
In CAD, you can create a circle by specifying both vertices of a cylinder, but in blender, you won’t have that function.