Madonna became famous about 1 year after her first single, “Everybody,” was released in 1982; her first big mainstream hit was “Holiday” in 1983.

Quick timeline

  • 1982: “Everybody,” her debut single, was released, but it was more of a club track than a major pop breakout.
  • 1983: “Holiday” gave her the wider public breakthrough and pushed her into real pop stardom.
  • 1984: By the time Like a Virgin came out, she was fully a superstar.

Plain answer

So the short answer is: around a year after her first song, though she was already building attention before that through clubs and early singles.

TL;DR: first single in 1982, fame breakthrough in 1983, so roughly 12 months.