Test if object is within collider bounds on start

Hey Unitarians!

Fairly simple question, but I couldn't find the answer anywhere, nor in the documentation.

What I have is a missile that is instantiated when the player fires it. I have a sphere Collider on the object. I want is so that when it detects an enemy, it locks on as a target and homes into it. Checking to see whether an enemy has entered and turning it into a target is easy. I use this script:

 using UnityEngine;
 using System.Collections;
 
 public class PlayerRocketRangeChecker : MonoBehaviour {
 
     public Transform target;
 
     void OnTriggerEnter (Collider other) {
         if(other.gameObject.tag == "Enemy") {
             target = other.gameObject.transform;
         }
     }
     
     void OnTriggerExit (Collider other) {
         if(other.gameObject.transform == target) {
             target = null;
         }
     }
 }
 

However, this poses a problem. If the player shoots the missile when it is really close to the enemy, the missile fails to lock in, because it starts off with the enemy within its collider.

So is there a way to check to see if an enemy is inside the collider on start?