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 Phyrexian Altar by sacrificing the persist or undying creature, adding one mana of any color.
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.