Function has option for short date (Ymd) and to change the divider for short date.

Random date between two dates.js

/**
 * Get random date between two dates
 *
 * @param {Date} start earliest date
 * @param {Date} [end=today] latest date
 * @param {boolean} [short=false] only get Ymd (as string)
 * @param {string} [join='-'] divider for short date
 *
 * @returns {Date|string}
 */
function randomDate(start, end = new Date(), short = false, join = '-') {
    const d = new Date(start.getTime() + Math.random() * (end.getTime() - start.getTime()));

    if (short) {
        let year = d.getFullYear(),
            month = '' + (d.getMonth() + 1),
            day = '' + d.getDate();

        if (month.length < 2) month = '0' + month;
        if (day.length < 2) day = '0' + day;

        return [year, month, day].join(join);
    }

    return d;
}

const startDate = new Date(2012, 0, 1);
const endDate = new Date(2020, 11, 31);

console.log("between: 2010-01-01, and: today\n\t=>\t", randomDate(startDate));
console.log("\nbetween: 2010-01-01, and: 2020-12-31\n\t=>\t", randomDate(startDate, endDate));
console.log("\nbetween: 2010-01-01, and: 2020-12-31, as: short\n\t=>\t", randomDate(startDate, endDate, true));
console.log("\nbetween: 2010-01-01, and: 2020-12-31, as: short, divider: none\n\t=>\t", randomDate(startDate, endDate, true, ''));