If anything in the previous incarnations of Elite is considered canonical, then the frame shift drive did not exist in 3250-3255, when First Encounters was set. Back then, people travelled through "hyperspace" using "hyperdrives": faster than light, but a whole lot slower than the current FSD. According to the galactic timeline printed in the "Gazetteer" lorebook included with the Elite II Frontier game, the hyperdrive was discovered circa 2100 and initial expansion into the galaxy was slow. In 3200-3250 (FE2 and FFE), it used to take 1 game week to travel the max distance your ship could travel in 1 jump; in a fast ship like an Asp, it took 1 game year to travel out to the edge of explored space (1000 LY from Sol) and back.
Now, with FSD, you can travel those same distances in a pleasant afternoon's cruising, and the far side of the galaxy is only a couple of weeks away. I think the only thing stopping the human race exploding out beyond the Bubble is the birth rate, since travel time is no longer an obstacle. I would assume when the FSD was invented, all the starships then in existence were promptly recalled and refitted with the new tech.
The phrasing of some of the promotional material for the game, along the lines of "With the advent of the frame shift drive, there's never been a better time to explore the galaxy", also implies that the FSD is a very new invention. Again, assuming that's a canonical statement, and not just marketing hype by FDev.