And Ms. Abrams’s race and gender may make her bid difficult enough: Georgia has never elected a female governor, and while Atlanta has elected a procession of African-American mayors, they have not found success in running for statewide office.

Many Democrats believe that waging a progressive campaign aimed at mobilizing liberals, rather than running toward the center to win over suburban moderates, is folly in a state that has not elected a Democratic governor since 1998.

“It’s still a red state, even though it’s getting more purple every year,” said Kerwin Swint, chairman of the political science department at Kennesaw State University.

Yet Ms. Abrams’s candidacy comes at a volatile moment in Georgia, where demographic changes are creating fresh uncertainty about Republicans’ dominance, and when left-leaning voters are highly energized.

President Trump carried Georgia by just five percentage points in 2016, a narrower margin than he enjoyed in traditional battleground states like Ohio and Iowa. And booming communities of black, Hispanic and Asian-American voters in the Atlanta area have put Georgia on track to become a majority-minority state inside of a decade.

Her candidacy will also be a test of whether the extraordinary energy coursing through Democratic politics at the federal level will also flow into state elections. In a special election for Congress in Georgia last year, grass-roots donors helped a political newcomer, Jon Ossoff, raise nearly $30 million in a losing campaign. But there is little precedent for Democrats pouring small dollars into a state election on that scale, and it is unclear whether Ms. Abrams can expect a similar outpouring of support.

Recognizing that opportunity, and facing growing calls for candidate diversity in a party that depends heavily on black voters, several national groups aligned with Democrats have made Ms. Abrams’s campaign a top priority. And African-American activists say they will be watching them to ensure they keep their commitment.