Gotti wasn't immediately made boss but at a meeting of all the capos not long after Big Paul was hit nobody dissented when he proposed himself as the new boss. Gotti had a lot of muscle behind him (he just took out a boss) and nobody else wanted to end up like Paul or Bilotti.

Of course they couldn't tell the future, but a lot of guys in the Gambinos had tired of Paul's "unfair" share of the profits that the family made, especially off of the loan sharking and gambling which he didn't have as large a hand in. When Gotti took over it was perceived to be "back to the streets" so to speak.