If a persist creature is used, it does not have a -1/-1 counter on it.
Otherwise, if an undying creature is used, it does not have a +1/+1 counter on it.
Steps
Activate Ashnod's Altar by sacrificing the persist or undying creature, adding ({C} magic symbol) ({C} magic symbol) .
When the creature dies, its persist or undying ability triggers, returning it from your graveyard to the battlefield without a -1/-1 counter or a +1/+1 counter on it due to Solemnity.