Well for me it depends.
If you are asking in reference to how long it took to make a billion on the market, or if you are asking how long into playing did it take me to make a billion.
I didn't start playing the market till about a year plus into my eve career. I basically did a tone of missions in this time and then met a few people and went out into 0.0 when soverinty was new and BoB was in full prevelance.
A billion wasn't really a personal objective, more making sure I had sufficient to replace my next loss (Which were huge) I typically had about 350M in my wallet, with no interest in exceeding this balance.
Then one day I decided to buy another account or two to try different things. This is when I started playing the market. I had just been given my own moon by alliance for my contributions to war effort and basically I had my 300M in my wallet and about 2 weeks of Moon Goo to start. Next day I had ~750M, that day I was ratting in and I had an officer spawn and to my delight he dropped 3 mods worth over 2Bill.
However same thing as on the market Money makes money, OP's initial 50M donation probably saved you 2 to 3 weeks of game time. And for me my experiences in PVP/PVE greately shortend my rise in financial wealth.
If I started out playing the market from the word go it would no doubt have taken me months to get there.
In my years in eve I too have been the benefactor of some sweet deals, a numpty who got the wrong number of 0's on a chimera contract leaving me with a fully fitted Chimera for 107M rather than 1.07B springs to mind. On the other side I have also been scammed twice, once costing me 80M isk and another 400M isk both fairly early on in my carrer which hurt, but would of hurt much more if I hadn't had the moon making money for me. so it is swings and round abouts.
This is going to be very different for people in general dependant on certain factors.
Starting Capital, if you have a benefactor or another character feeding you your starting capital
personal Wealth (a few traders I know started the game recently by buying in like you would at a poker table) basically dropping a GTC into their wallet to give them half a bill starting
Time, I rarely spend more than a few hours a week on the market these days, things to do people to kill! I know I could make substanitally more was I not working or could dedicate more time to eve.
Financial inclination, if you have a job in Finance or natural head for figures will give you advantages,
Luck (speaks for itself)
Friends, to help you and show the ropes
Patience, Trading can be infuriating.
Drawing sources, if Market is your sole reason for eve it will be 0, but for most players the market is a means to fuel their PVP or other endeavours.
Attitude to Risk, high risk means more profit, but more chance for loss, a luck person could make a Bill fairly quickly, and unlikely person may never get there. A risk adverse player would get there but may take a long time to do so.