I am not sure I understand your question correctly.
In general you can set timescale = 0 and back to 1 to continue playback where you just stopped. You can also query and store playback time via TrackEntry.TrackTime.

In Unity the following code implements what is described above:

using System.Collections;
using UnityEngine;
using Spine.Unity;

public class AnimationStateTesting : MonoBehaviour
{
   IEnumerator Start() {
      SkeletonAnimation skeletonAnimation = this.GetComponent<SkeletonAnimation>();
      yield return new WaitForSeconds(1);

  // Pauses playback
  skeletonAnimation.AnimationState.TimeScale = 0;
  float savedTrackTime01 = skeletonAnimation.AnimationState.Tracks.Items[0].TrackTime;
  yield return new WaitForSeconds(1);

  // Resumes playback
  skeletonAnimation.AnimationState.TimeScale = 1;
  yield return new WaitForSeconds(1);

  // Sets playback position of first track to saved pause position.
  // Note that this is a simple version for only a single track, which also does not
  // respect if a different animation is already playing.
  skeletonAnimation.AnimationState.Tracks.Items[0].TrackTime = savedTrackTime01;
   }
}