Of course, in a race likely to stretch over the next 18 months, early advantages can dissipate quickly. A strong poll or viral moment can prompt donors to give to new candidates, thereby growing their lists by huge numbers — so long as they are positioned to capitalize. Ms. Harris’s launch-day haul, for instance, rivaled that of Mr. Sanders in 2015.

Ms. Dunn said she saw the initial rankings less as a predictor for the coming primary’s outcome and more as a revealing indicator of “who was able to use their 2017 and 2018 effectively to prepare for a presidential race.”

Both Ms. Harris and Ms. Gillibrand landed on the leader board despite having not faced a competitive election in recent years. The two senators spent heavily to bulk up their small donor lists, investing in multimillion-dollar campaigns on Facebook in 2017 and 2018 to add email addresses to their supporter list and lure in new contributors.

“It’s almost like growing vegetables,” said Tim Lim, a veteran Democratic digital strategist. “You have to be mindful. You have to be aware of major events. You have to be patient. But then, within six months or so, your investment will pay back.”

While it is no surprise that Mr. Sanders is ahead with small digital donors — he is the only potential candidate to have a previous run for president included in the analysis — the sheer magnitude of his opening advantage is striking.

Mr. Sanders had 369 days during his 2016 presidential campaign where he processed more online donations than Ms. Gillibrand did on her single best day in the Senate — the day after President Trump tweeted about her “begging” him for money — through the end of 2018, according to the data. (Ms. Gillibrand’s biggest days were notably smaller than those of her rivals with large bases of support.)

The advantage that Mr. Sanders and Mr. O’Rourke enjoy is not just the size of their lists but the exclusivity of their donors — the vast majority of whom (an estimated 87 percent for Mr. Sanders, 72 percent for Mr. O’Rourke) have not contributed to any other potential 2020 candidate. In contrast, less than half of Ms. Warren’s donors have given only to her among the potential 2020 field.