Shakespeare lived during the Renaissance period which brought forth a revival of interest in classical Greek and Roman ideas, thinking, and literature. Elizabethan England was also influenced by Christianity and paganism coming out of the medieval period. All of these ideas come together in many of Shakespeare's plays and Romeo and Juliet is not excluded.
One Greco-Roman idea is that Fate determines one's destiny, not the individual. Hence, there is absolutely no way for a character in a play or piece of literature from that time period to conquer Fate. No matter what the hero or heroine does, he or she cannot overcome the path that Fate has set forth for their life or their death. The famous classical play Oedipus Rex is a perfect example of a hero trying to run away from his fate but then finds out that he actually runs towards it. The same is true for Romeo and Juliet. No matter what they do, no matter how they try to get around obstacles, they cannot change what is stated in the prologue about their love being "star-cross'd."
This image comes from Greek and Roman heroes being eternalized in the stars for their heroism, courage, and valiant lives; a star-crossed person means that their life will not be written or remembered in the stars. It's just not meant to be, basically, and Fate makes its presence and mind known right before Romeo and Juliet even starts. No matter what anyone does to change the way things will end, whether it's Friar Lawrence or the lovers, there's absolutely no way that they have any control over the path they will travel towards their deaths. So, yes, the tragedy was completely controlled by Fate. There are some places where it might seem that free will is being used to counter-attack Fate's path, but just like Oedipus, these attempts only help drive the characters towards their fate and not away from it.