Sol is the closest target.Any guess how many expensions we'll need to achieve our goal?
With perfectly controlled targeted expansions it could be done in 3.
With completely uncontrolled expansions it would take about 1000 on average.
If you obtain sufficient control to always expand from the system you're in that's closest to Sol (or, while in the process of capturing that system, somewhere nearby that helps direct future expansions), somewhere in the 20-50 range is plausible and lower is possible.
From Sol it's not that much further to LFT 509 - another 2 perfectly targeted or 10-30 with moderate control.
Lave is then in a completely different direction but by then you should know what you're doing.