Yet absent, at least so far, is either an obvious political phenom like former President Barack Obama or an establishment-backed juggernaut in the mold of Hillary Clinton. Unlike the last few Democratic primaries, the unsettled race evokes the sprawling nomination fights of earlier decades — lacking a dominant figure and seemingly inviting new leaders to rise.

“The opportunity for somebody to emerge and catch a wave hasn’t been this high since 1976,” said Anita Dunn, a veteran Democratic strategist, referring to another unpredictable primary featuring a multitude of candidates and a party wrestling with its identity.

Interviews with about four dozen lawmakers, consultants and party leaders revealed a mood of emphatic uncertainty: Senior Democrats see their party in a historically volatile state, and they are wary of attempting another Clinton-style coronation. But many Democrats believe the party’s turn left, combined with the rising fury of progressive women and the grass-roots appetite for a political brawler, have created an especially inviting environment for Ms. Warren.