That's the idea.
We can also have third party protagonists and antagonists, as was mentioned. I had an idea for a storyline revolving around a mysterious Crimson King, whom the heroes would eventually
plot details within
I think that would fit here nicely.
How about this idea; we bring everyone together into one time period, but individually RP through each life stage up until the desired one. (Hatchling, Whelp, Young, Adult, Ancient, Twilight.) Dragons of similar ages would encounter one another while growing up.
Alternatively, just start people out at whatever age. (Though Ancient and up would be up to the host's discretion, as an ancient dragon in DnD is a level 26 to 30 solo monster. E.g., a challenge for five near-demigods.