In the context of the play, Frank and Charley are playing this song as an audition piece for the Blob, this nightmare mishmash of American vapidity and excess that are the 'taste makers'—they have no distinct personality, just blindly following what's 'in.'
Immediately after they play "Good Thing Going," Frank succumbs to the Blob's pressure to play it again—despite Charley's explicit warning not to. True greatness, he cautions, is knowing when to leave. But Frank is too delighted that the Blob is finally approving him. He convinces Charley to play again, but the spell's broken—the Blob has heard it before—it's no longer new. They talk over it this time, hum along, and eventually drown the song out entirely.
Let's clarify. Remember, this show runs backwards in time. So, Act One, the first time we hear "Good Thing Going" is at the top of "Franklin Shepard Inc." We don't hear the whole song, but a clip, and Franklin and Charley are being interviewed about their place in musical theater history because, largely, of a career that includes "Good Thing Going." The next chance we have of hearing it is the start of Act Two, Gussie's Opening Number—this is the moment that "the world" got to hear and fall in love with this song. THEN we get to the Blob, actually hearing "Good Thing Going" for the first time, and then the Blob taking it over. So now we can see the full story in reverse—they were young kids very excited to create this song, played it for producers who changed it and made it glossier, and Franklin kept chasing the high of that first time he played it, but to diminishing returns.
And so, the song carries all those scars with it as you hear "We started out like a song... we started quiet and slow."
Not only did they (Frank, Charley, and Mary) start out like a song—they started out like that song—they had a good thing going—the song had a good thing going. Going, gone. The song becomes a stand-in for everything Frank and Charley were trying to build together. They were the good thing going—their friendship, their creative partnership, their shared vision. But, just like the song, their collaboration loses its spark and gets overshadowed by external pressures.
And of course, it ACTUALLY starts in bits and fragments in "Opening Doors" (which is one of the last songs after the Blob), this time because they're creating them, not because they've become corrupted. Also, the typewriter and keyboard are playing together like Charley says they SHOULD be in "Franklin Shepard Inc."
Anyway, apparently the Blob thing is something that Sondheim experienced personally at a party, which I always really liked as a note. They also very specifically chose young actors to capture the energy of the main characters as they were starting out in life.
In the documentary "Best Worst Thing That Ever Could Have Happened," Lonny Price (Charley) talked about how it was all of these kids' dreams coming true, and they felt like they were living the musical. That certainly seems to have been intentional as part of the casting as well.
Final piece: Lonny Price tells this story where the cast members were having a party, and Sondheim caught wind of it and asked if he could come along (they hadn't invited him because they didn't think Sondheim—god Sondheim—would want to hang out with a bunch of kids). But apparently not only did he show up, he showed up to play them a song he had just finished writing—"Good Thing Going." Lonny miraculously had a tape recorder, and yes, the room is enrapt and nobody asks him to play it again, effectively bringing to life the moment that we first hear the song in the play, but for the kids that were in the cast. He gives them this moment to show that this is the theater, and 'they're really in it' and for now, the good thing is here. It's going to keep going and going until it's gone. I haven't been able to hear the song the same way since I saw the documentary.