After doing some exhaustive research, I think I've finally managed to pin down a definitive timeline of the 'Heroes' universe leading up to the events of the first season. It's amazing, the way they scattered so many tiny clues in the series itself, but I think I've managed to unravel them all. (Warning: This timeline will contain spoilers for the events of season one. I'd recommend that you not read this until you've seen all of the first season. Mainly because none of this will make any sense otherwise.)
1955: Alien plants use a total eclipse of the sun (a recurring motif of the series) to teleport a seedling of theirs to Earth, as part of a plot to wipe out the human race. The seedling is destroyed by Seymour Krelbourn and Audrey Gray, but the pollen of the alien plant turns out to have a mutagenic effect on human beings. Pollen contamination will cause spectacular mutagenic effects over the next decade.
1956: Seymour and Audrey marry and move to the suburbs.
1957: Tolian Soran, thought to have died in an explosion on Veridian 3, instead finds himself in New York City during Earth's distant past. During the brief period he spent within the Nexus (prior to Jean-Luc Picard and James T. Kirk's alteration of history), he communed with a mysterious entity that claimed to be trapped within a black hole. In exchange for a promise of assistance in escaping the black hole, the entity helps Soran time-travel away. Soran takes the identity of "Linderman". At this time, he is contaminated by alien pollen, developing the ability to heal.
1958: Seymour Krelbourn dies from radical mutations developed in the wake of overexposure to the alien pollen. Audrey Gray breaks with tradition by reverting to her maiden name, and moves back to her old neighborhood in New York to raise her newborn child, whom she names Gabriel. In order to prevent him from taking an interest in botany (which she irrationally blames for her husband's death), she tells Gabriel that his father was a watchmaker.
1972: After several misadventures, including a tour of duty in Vietnam, Soran finally frees the renegade Time Lord known only as "The Master" from the black hole he was trapped in, and uses his powers to stabilize the Master's decaying human host. Soran/Linderman and the Master embark on an ambitious scheme to alter the course of human history using the alien pollen to catalyze the next stage of human evolution.
1975: After his return from Africa, John Shaft develops prcognitive dreams due to exposure to alien pollen; deciding to use the ability to make himself wealthy, he develops the identity of "Charles Deveaux". He spends many years acumulating wealth and power, and reluctantly lends his talents to Soran/Linderman on occasion; despite his money, though, nobody understands him but his woman.
1983: Captain Hikaru Sulu, of the starship Excelsior, is asked to take on a dangerous mission by Starfleet involving the apprehension of criminals attempting to alter the course of human history. Upon arriving in the past, however, Sulu recognizes that the alterations are too great to stop by simply capturing the criminals, and embarks on a long-term scheme to minimize their damage to the timestream. To this end, he begins building a corporate empire in Japan and makes the acquaintance of Soran/Linderman.
1987: By this time, the Master's "black ops" organization that complements Soran/Linderman is fully up and running, using both regular humans and those whose DNA has been altered by the alien pollen. The Master, calling himself "Thompson", recruits as his newest operative a man called "Claude." Unbeknownst to the Master, "Claude" is actually his old nemesis, the Doctor, who has regenerated since the last time the two met and has used the newly-installed 'chameleon arch' in his TARDIS to create a false persona for himself to allay the Master's suspicions. He does take the extra step, however, of installing "Claude" with pollen-altered DNA, giving himself the ability to become invisible.
1991: Lana Lang graduates from Shuster University and takes a job at the Bureau for Extra-Normal Matters in Capitol City, Florida.
1993: Lana Lang severs her ties both with Clark Kent and Superboy, and uses her connections at the Bureau for Extra-Normal Matters to obtain a job with the FBI, specializing in cases of unusual serial killers.
1999: John Connor, on the run from robotic killing machines from an alternate future known as "Terminators", takes the identity of "Zach" while living in Texas. He will hide under this identity for several years.
2000: Having trusted the wrong person in Thompson/The Master's black-ops group (known as "The Company"), Claude/The Doctor is badly injured. Failing to remember his true Time Lord heritage, he spends the next several years on the run (which, in turn, causes him to resolve never to use the chameleon arch without entrusting his secret to a partner in the event of mishap.)
December 2005: Eric Weiss, CIA agent, goes deep undercover as an LA beat cop, complete with marriage. Unbeknownst to him, however, he has been exposed to alien pollen.
April 2006: Chandra Suresh approaches Gabriel Gray, having determined that his DNA contains the markers that will allow him to detect people who have developed "super-powers". Gray's DNA, which was affected by massive doses of pollen on both his mother's and father's side, is indeed powerfully mutated (despite his mother's never having developed any powers at all from her exposure to alien pollen.)
September 2006: Heroes begins.