If you are Jewish, you might have a better chance of leaving as a limited numbers of them were allowed to officially immigrate (250,000 at its highest) after the passage of Jackson–Vanik amendment and Strategic Arms Limitation Talks. In August 1975, at a summit conference held in Helsinki, the two leaders agreed to recognize the postwar boundaries of Western and Eastern Europe. Brezhnev agreed to permit more Soviet Jews to emigrate in exchange of grain exports and some high tech imports (Read more in The United States under Ford and Carter).
You will need to apply for an exit visa first, which was seen as an act of treason and have a high social consequences as you would need to quit your job but avoid been seen as "social parasite" (not having a job is a criminal offense). Usually one would need a relative living in another country for sponsorship and a letter of recommendation from one's own workplace. In Gary Shteyngart's memoir Little Failure the author described even his senile grandmother had to sign documents that would permit her adult daughter to emigrate. His parents also did not tell him about their plans for immigration for fear that he might accidentally tell the wrong people and cause their exit visa to get cancelled.
(People who quit their jobs but refused an exit visa were called "Refuseniks", they often ended up getting detained for a variety of charges).
You may be interested in the case of Adolf Georgievich Tolkachev, who worked on Soviet military radar systems that would go into MiGs and such. While it seems almost comically risky in hindsight, his method was to walk up to cars at gas stations with US diplomatic plates and leave a note saying he wanted to:
. . . “discuss matters” on a “strictly confidential” basis with an “appropriate American official.”
He did this several times, but the CIA was wary of KGB counterintelligence ops. On one attempt, Tolkachev happened to get the local CIA chief. Once they were satisfied that he was ligit, he passed along advanced R&D data on radar systems and other military hardware projects. In particular, a passive phased array radar for the MiG-31 Foxhound.
Tolkachev seemed intent to stay in the USSR and keep passing information for as long as possible. He turned down several extraction plans. Eventually, the Soviets tracked him down, and the CIA was not able to extract him in time. He was executed, though his family survived.