You choose whether to put +1/+1 counters on the creature or create a Spirit token as the ability that includes the endure instruction is resolving. No player may take actions between the time you choose and the time that counters are added or tokens are created.

If you can’t put +1/+1 counters on the creature for any reason as an endure ability resolves (for example, if the creature is no longer on the battlefield), you’ll just create a Spirit token.

If a noncreature permanent is instructed to endure, the effect is the same. You can put +1/+1 counters on that permanent or create a Spirit token.