This is a question I've had for awhile also. The best way I found to figure that out, is by the dialogue and also what the shuttle looks like that drops the platform. Most of the pictures online of Serenity's shuttles look like it has longer wings than the rescue shuttle, hinting at a different ship. On the other hand, some of the pictures show a shuttle without wings, so maybe that's the one they use. We all know there are at least 2 shuttles on Serenity.
The dialogue in the rescue doesn't really set a time period either, though at no point in time does the scientist make mention of being getting her back.
In my opinion, the opening scene does 2 things, shows new viewers the history and gives old viewers a fun view of how he rescued her.