Can you get Zen without paying in Star Trek Online?

Yes. You can earn Dilithium through play, refine it, and use the Dilithium Exchange to place an offer for Zen sold by other players. Buying Zen with real money is not the only route.

Direct Answer

Use Refined Dilithium on the Dilithium Exchange

Player exchange

You can trade Refined Dilithium for Zen.

The Dilithium Exchange is a player market. You place an offer using Refined Dilithium, and another player supplies the Zen. The market can fill an offer immediately or leave it waiting in the queue.

Sources checked: Epic Games: STO FAQ · STO Wiki: Zen · STO Wiki: Dilithium Exchange

How It Works

From gameplay currency to Zen

Four steps

You need Refined Dilithium before you can place a Zen buy offer.

Earn Dilithium Ore→Refine it→Place a Zen offer→Receive Zen when the offer fills

Exchange Backlog