The best I'm seeing is 10 months to recoup the cost of a facility at market values and maximum trading skill used. So Facilities is not the best way, unless you can buy them at a good price and flip them for a profit.
Warning this is strictly Orions McPhees Opinion, it may or may not have any bearing on events true or imagined
Fastest way is by trading, yet it is also time-comsuming to get a lot of money, and you need to be an active player and a social person.
What you need to do:
1) Keep up to date with average market prices of things
2) Check the open markets and stay in contact with people selling stuff
3) When you see the opprotunity to buy something for under its market price, buy it.
4) Sell it at a profit.
Depending on what you trade in and what circles you move in, you can get a profit of at least 5-10%, and up to 20% if you buy in bulk and sell things off independently. You can even get 30-50% profit if you move in the appropriate circles.
So, if you start trading with, say 5000 credits, and make a couple of trades a week, you could grow the amount of money you get each month out of faction exponentially from <1000 credits to 100,000 or even 1 million