Also wasn't most of season 3 of"TNG" made up of writers except for Behr who got their jobs like this by the time the season ended? Not counting someone like Snodgrass who left before the season ended.
Ira Steven Behr: asked by Michael Piller to join and help supervise the writing staff. First job was performing a "major" rewrite on The Hunted.
Hans Beimler: wrote for the show for the first 3 seasons, starting with Coming of Age. Left after season 3 partly because of personality clashes with Michael Piller.
Richard Manning: wrote for the show for the first 3 seasons, starting with Coming of Age. Left after season 3 partly because of personality clashes with Michael Piller.
Melinda Snodgrass: sold the first unsolicited script for TNG (Measure of a Man). Left after season 3 partly because of personality clashes with Michael Piller.
Richard Danus: Worked on the first 10 weeks of season 3's production. Contract not picked up. Later wrote for DS9.
Ronald D. Moore: like Snodgrass, sold an unsolicited script for the series sometime during season 2. Wasn't asked to join the staff until season 3.
Michael Wagner: staff writer for the first four episodes of season 3 before leaving production.
Hanna Louise Shearer: wrote for the show since the first season. Last credit with the series was episode 308, The Price.
Rene Echevarria: sold The Offspring as an unsolicited script, bungled the rewrite and wasn't asked to join the writing staff until late in season 3.
Shari Goodhartz: writing staff intern during the back half of season 3.
This doesn't count the one-and-done credited writers that already had established careers as television writers. Overall, only Moore and Echevarria became staff writers as a result of the open submission policy.
EDIT: Looks like
@Lord Garth beat me to it.