The Sovereign Project could have taken just as long to get from drawing board to space as the Galaxy-class which took almost 15 years to get from drawing board to space. (2343 to 2357 when USS Galaxy is launched). But perhaps not as long in the prototype testing as the Project would use more tried and tested equipment than the Galaxy-class did. It took five years before USS Yamato and Enterprise were launched after Galaxy. Was probably not as long between the launch of Sovereign to the launch of Enterprise...assuming they didn't rename Sovereign to Enterprise on launch.
I don't know guys. In First Contact we suddenly see a ton of new designs. I find it difficult to believe that all of these ships were 'in the works' for decades then all happened to roll off the assembly line at the same time. My personal theory is that it must be no more thatn a few years from design to service, albeit that does stretch credulity compared to the build cycle from today's Navy.
With the technology available to them, it shouldn't take more than a year, maybe two at the absolute most to build any ship. It's only the design process which would take a long time, since you want to make absolutely certain you don't overlook any stupid mistakes. It's possible the normal design process can last up to twenty years, although that actually sounds pretty long to me, but I don't see any reason why it would be truly necessary for it to take that long. If we assume that the explosion of new ship designs is largely a reaction to the Borg threat (and later the Dominion threat), which is what we're usually told on screen, then there have been eight years of development time since the Federation's first contact with the Borg.
If we assume that some of the 'new' designs are actually modifications/repurposing of older designs, maybe in some cases even pulling old ideas out of the archives that were rejected in the past because the Federation doesn't build 'warships', so that many of them wouldn't even have to have been designed from the ground up, and that the truly brand new designs are mostly smaller, simpler ships like the Defiant (which according to Memory Alpha was designed in 2366 and launched in 2370) then it seems to me like they had plenty of time to get all those new classes out there.
There's also no reason to assume that all these new designs rolled off the assembly line just in time for FC. Some of them could have been serving for years already and we just never saw them before. I don't recall any really huge fleet battle scenes where you would expect to see that sort of thing until the height of the Dominion War (after FC).