You are right about the disadvantages of being born in Serbia (Yugoslavia back then) as you can't compare the quality of tennis facilities and financial support the local clubs or young talents receive from the national tennis association, so in that sense people born in USA, Switzerland, Spain etc were "luckier".
On the other hand, he was very lucky to be noticed by Jelena Gencic (by her own testimony, she saw a little boy sitting and watching her coaching other kids, so she was curious and asked him if he wants to join, which he was thrilled to accept) and basically started to be coached by the Yugoslav Nick Bollettieri for juniors, by far the best tennis coach for your players in the country, who discovered and coached many talents (Seles, Ivanisevic, Majoli). The price his parents had to pay was probably very symbolic and he immediately received a high quality treatment. Furthermore, Jelena helped him enormously to develop his later career by convincing Pilic to accept him to his academy.
How many players (Easterners or Westerners) had to luxury to get by far the best junior coach in the country, who trained them literally pro bono? Not many. So in that sense, he was lucky.
By the way, I don't know how you came up with the two years latency, but you are probably right lol. Gencic used the very same number while talking about his inability to travel and play tournaments, due to financial reasons, when he was 17, so it definitely slowed him career down a bit.
Anyway, nothing is black and white and the same goes with the Djokovic story.