Expert question - I want to find out the vector of the lowest vertex from the centre point of an object

Here is some code to help you out:

 using UnityEngine;
 
 public class MyScript : MonoBehaviour 
 {
     public MeshFilter meshFilter;
 
     private Vector3 lowestVertex;
     private Vector3 center;
 
     private void Start()
     {
         if(meshFilter == null || meshFilter.sharedMesh == null)
             return; // TODO: Error feedback.
         
         lowestVertex = FindLowestVertex();
         center = FindCenter();
     }
 
     private Vector3 FindLowestVertex()
     {
         float lowestYCoordinate = float.PositiveInfinity;
         var lowestVertex = meshFilter.transform.position; // Some sensible default.
 
         var vertices = meshFilter.sharedMesh.vertices;
         for (int i = 0; i < vertices.Length; i++) 
         {
             // Check for the lowest position in world space.
             Vector3 worldCoord = meshFilter.transform.TransformPoint(vertices[i]);
             if(worldCoord.y < lowestYCoordinate)
             {
                 lowestYCoordinate = worldCoord.y;
                 lowestVertex = meshFilter.transform.InverseTransformPoint(worldCoord);
             }
         }
         return lowestVertex; // In local space.
     }
 
     private Vector3 FindCenter()
     {
         Vector3 center = meshFilter.transform.position;
         Vector3 sum = Vector3.zero;
         var vertices = meshFilter.sharedMesh.vertices;
         for (int i = 0; i < vertices.Length; i++) 
         {
             sum += vertices[i];
         }
         center = sum / vertices.Length;
         return center;
     }
 
     private void FixedUpdate()
     {
         Vector3 centerWorld = meshFilter.transform.TransformPoint(center);
 
         Debug.DrawLine(
             centerWorld + new Vector3(0, -0.1f, 0), 
             centerWorld + new Vector3(0, +0.1f, 0), 
             Color.red);
         
         Debug.DrawLine(
             centerWorld + new Vector3(-0.1f, 0, 0), 
             centerWorld + new Vector3(+0.1f, 0, 0), 
             Color.red);
 
         Vector3 origin = meshFilter.transform.TransformPoint(lowestVertex);
         Debug.DrawRay(origin, Vector3.down, Color.green);
         // TODO: Raycast
     }
 }
 

"Any object" is a little too broad, so I assumed you were talking about meshes. If you don't use the transform as a pivot, you can take the average of all vertices to find a center position.

To find the lowest vertex position in a mesh you have to loop through all the vertices and compare each one.