At what point in Deep Space Nine did Voyager disembark for their mission?

Just curious because in Message In A Bottle, The Doctor is back in the Alpha Quadrant temporarily and says something like "What's the Dominion?"

I thought Voyager season 1 started alongside Deep Space Nine season 3, where all anyone can talk about is fear of a Dominion invasion, even at it's very beginning. The Dominion was even whispered about and discovered in season 2. I think at least Janeway and the Starfleet people would tell the other crew about it. Lots of free time for talk that would eventually lead to The Doctor. But I think The Odyssey getting destroyed would be huge news.

Let me know if I have the timelines wrong, or if it was just a choice to have The Doctor in the dark on this.