WEST DES MOINES, Iowa — It was game time at the “Persist Party.”

Grace Smith, a 23-year-old field organizer for Senator Elizabeth Warren’s presidential campaign, outlined the rules. The dozen or so Iowans gathered in a volunteer’s family room would split into two teams, pick paper slips from a bag and try to get their teammates to guess what was on them.

Many of the words and phrases on the slips reflected the vocabulary of Ms. Warren’s presidential bid: Break up big tech. Ultra-millionaire wealth tax. Student debt cancellation. Impeachment. When the game ended, “Persist” koozies were awarded to the winners.

Ms. Smith is one of about 50 paid staff members Ms. Warren’s campaign already has on the ground in Iowa, far more than any other Democratic candidate is known to have hired in the state. The growing Warren juggernaut reflects a bet that rapidly hiring a large staff of organizers will give the senator an advantage over her rivals who are ramping up their efforts at a slower pace.

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The strategy does not come cheap. Ms. Warren’s campaign spent more than $5 million over the first three months of the year, the most in the field, according to Federal Election Commission records. Her payroll included about 160 people during that period, far more than any other Democrat’s. Her team says its staff has grown even larger since then, to more than 200 people, over half of whom are based in early-voting states​.