Immediately begins a drag as soon as a mouse/finger down event occurs on a Unity UI object.

BeginDragImmediately.cs

using UnityEngine;
using UnityEngine.EventSystems;

public class BeginDragImmediately : MonoBehavior, IInitializePotentialDragHandler, IBeginDragHandler, IDragHandler {
    public void OnInitializePotentialDrag(PointerEventData eventData) {
        eventData.pointerDrag = gameObject;
        eventData.dragging = true;
        eventData.useDragThreshold = false;
        ExecuteEvents.ExecuteHierarchy(transform.gameObject, eventData, ExecuteEvents.beginDragHandler);
    }
    
    public void OnBeginDrag(PointerEventData eventData) {
        // Only required if your Drag function is what sets the position of the gameobject
        HandleDrag(eventData);
    }

    public void OnDrag(PointerEventData eventData) {
        HandleDrag(eventData);
    }

    void HandleDrag(PointerEventData eventData) {
        // Set position here
    }
}