Hello
I don't see a simple method or function to do this.
With the 4 points I will make a volume from which I will obtain the center of mass.
From this point and two of the initial points, I will make a plan and then a sketch to make the sphere with one revolution
not really 
you can make a circle but an infinity of spheres
Unless the center is one of the points. And again with a center you only need 2 points
And yes, but the question concerns a sphere passing through 4 points 
Another method (maybe, since I'm not wide awake 
):
Fixed points at the desired coordinates in a 3D sketch,
A volume sphere from a 3D sketch with a piloted radius,
Add tangency constraints between the surface and the points.
In the absence of a quick method in SW, perhaps with this method:
For my part, I didn't watch everything, it's Monday morning!
Through four non-coplanar points A, B, C and D, it passes through a single sphere.
In fact, I have a polyhedron whose corners are defined by parameterization, it is inscribed in a sphere whose center I want to collect...
I would like not to leave SW... with an equation to deal with!
Hello
You take the first 3 points: A, B and C → you make a plane passing through the 3 points and you create the circle passing through these 3 points → you have a center → you draw the perpendicular to the plane passing through the center.
You take D, C and D (or rather B as @Sylk pointed out), you do the same → second straight line perpendicular to the second plane
Intersection of the 2 lines → center of the sphere (if SW allows you to create it with the curves...)
sphere 4 points. SLDPRT (138.3 KB)
Nb: it worked with the example attached in V2020
You meant B, C and D
It's not wrong 
A difficult start to Monday for many people obviously 
So I'm impressed!
Hello
Another solution...
In a 3D sketch, draw 4 segments from any unconstrained point P to the 4 points A, B, C, and D. Add an equality relationship on the lengths of the 4 segments, and you're done. P is the center of the sphere.
Yes... I will try!
Significantly easier to build than what I proposed (but I can feel SW putting red everywhere quite quickly in case of modifications).
Yes, it goes red from the beginning (impossible to put the equality at the 4 segments-> on direct constraint)
It works very well. You just have to put only the useful relationships:
That's exactly what I did @Sylk, but it was impossible to tie the 4 segments.
By redoing the manip no more worries it works very well.
Another subtlety of SW that escapes me? 
SW sometimes has hidden relationships, the little rascal 