I think after what I saw in Epilouge, I saw Destiny becoming a generational ship. The longer they were on it the less important home started to feel and they still contacted home because a of the stones. In terms of solving the mystery pattern, I’m kinda glad they didn’t because your setting yourself up to be disappointed. This would be such a massive discovery that anything less than massive, which is hard to define anyway, would still feel too small.
I like the idea of Destiny becoming a generational ship. Maybe inspired by their alternate lives in "Epiloque", the crew decide to start real families on board Destiny and we see, for example, Matt and Chloe get married and have a child on Destiny in S3. I would also envision each season Destiny exploring and having a positive impact on a different galaxy each season. Going to a new galaxy each season would allow for new stories and new aliens like we saw from S1 to S2. It would also mean that by the time we get to the series finale, the Destiny would have made a big impact on several galaxy, truly making a difference in the universe itself which would be really fitting for a series called "universe".
In terms of the series finale, I see a few options:
1) After several seasons of the Destiny making a difference in several galaxies, the series end similar to "Gauntlet". The crew has fully embraced that they are a generational ship with a mission to change the universe and they go off to the next galaxy... the end.
2) The Destiny and the crew sacrifice themselves to save an entire galaxy or even to save the entire universe from some cosmic threat.
3) The Destiny does finally return home to Earth but only after decades have gone by. The series finale could jump 50 years into the future where some of the original crew are still alive but old, some of their children born on the Destiny are grown up, and Destiny arrives back to Earth only to find things have changed a lot. And Destiny returns to Earth and saves the Earth from some problem. The End.
Personally, I prefer #3.
In terms of the Big Bang mystery, yeah, I can see how solving it could be disappointing. Even if you came up with something that sounded cool, it would probably only be cool the first time. But there would be a chance it would disappoint, especially if the audience had unrealistic expectations.
Brainstorming, I do see a few possibilities:
1) The pattern in the cosmic background radiation is evidence that the universe itself gained a form of intelligence shortly after the Big Bang. So the Universe itself is self-aware in a way.
2) The pattern is proof of God or some God-like being that existed at the beginning of the Universe. This option is probably the most problematic as it would probably run afoul of people's religious beliefs. And the Destiny meeting God or God-like Beings could be seen as bad taste or cheesy.
3) The pattern was created by Ascended beings in order to ensure their own existence. It's a self-fulfilling time loop. The Ancients long ago discovered the pattern which led them to build Destiny and eventually put them on the path to Ascension. No pattern, no Destiny and no Ascension. So the Ascended Beings created the pattern to create the timeline that would lead them to ascension.
4) Destiny somehow will create the pattern by going back to the beginning of the Big Bang. So Destiny is actually exploring their own signal.
5) Everybody was wrong. It was all a big misunderstanding and there was no intelligent pattern at all.
Personally, I like #1 and #3 the best.