Can you proliferate a poison counter on an opponent who has zero poison counters?

Proliferate means you choose any number of players and/or permanents that already have a counter on them, then put one additional counter of each kind that chosen player or permanent already has on them. This is defined in CR 701.27a.

The critical word is 'already have.' A player with zero poison counters has no poison counters on them, so they cannot be chosen as a target of proliferate for poison counters. You cannot use proliferate to introduce a new type of counter — it can only duplicate existing ones.

This applies symmetrically: you cannot proliferate experience counters onto a player who has none, energy counters onto a player who has none, or any other counter type that isn't already present on that player or permanent.

Concrete example: Your opponent has 0 poison counters and you activate Throne of Geth's proliferate ability. You may not choose your opponent to gain a poison counter, because they have no counters at all. However, if a different opponent has 3 poison counters, you may choose them, and they would go up to 4 poison counters.

The only way to give an opponent their first poison counter is through a source that specifically deals poison counters, such as a creature with the infect or poisonous ability (CR 702.90, 702.107).