But as white men, Mr. Biden, Mr. Sanders and Mr. O’Rourke do not reflect the gender and racial diversity of many Democratic candidates and swaths of the electorate that dominated the 2018 midterms. Ms. Harris, Ms. Warren, Ms. Gillibrand and Mr. Booker, by contrast, would instantly make the 2020 Democratic field the most diverse array of presidential candidates in history. And they might well scramble the early polling leads held by Mr. Biden and Mr. Sanders, who benefit from strong name recognition but would be in their late 70s by Election Day 2020, at a moment when some in the party are agitating for generational change.

The four senators hope that jumping into the race early will give them some organizational advantages in a contest that will almost certainly grow to more than a dozen candidates.

This kind of early frenetic activity — almost two years before the election — has happened before in primaries without a clear front-runner. At this time four years ago, many Republicans began preparing campaigns, wooing supporters and tacitly permitting fund-raising by allies in the wide-open race for the 2016 nomination, a contest that would ultimately attract more than a dozen candidates within months.

Already, at least two of the senators have nearly settled on close political lieutenants to serve as campaign managers, turning to male aides with whom they have deep and trusting personal relationships. Ms. Gillibrand is eyeing Jess Fassler, her current top aide, who is leaving his role in the Senate early in 2019, as a leading contender to manage her campaign. Ms. Harris is expected to name Juan Rodriguez, who helmed her campaign for the Senate in 2016, as her manager.

In a further sign of how developed her plans are, Ms. Harris’s aides are close to selecting Baltimore or Atlanta for her headquarters, according to people who have met with her team. She is likely to maintain a sizable office on the West Coast, perhaps in her native Oakland, but her political advisers have concluded that for practical reasons it is essential that she have a base in the Eastern Time zone.

Ms. Warren is expected to install Dan Geldon, her former chief of staff who was once her student at Harvard Law School and left her Senate office to plan her likely campaign, in a senior role directing campaign strategy. She has a head start on staffing: During the midterm campaign, Ms. Warren deployed staff to the four early primary states and a number of general election battlegrounds to elect other Democrats. Many of those organizers stayed involved after her re-election, leaving her with a staff of several dozen total.