Article One, the one that describes the form and function of the congress, does touch on the question by saying that voter qualifications in congressional elections must be no more – or less – restrictive than the standards the states set for those allowed to vote for "the most numerous branch" of that state's legislature. Thus the founders apparently presumed that there would be a set of standards by which states, and the union, would authorize the franchise, and from the beginning the constitution sets out to recognize that and place a floor under it.
Article one adds another quibble a couple of paragraphs later. It says that the "times, places and manner of holding elections for senators and representatives shall be prescribed the each state by the legislature thereof; but congress may at any time by law make or alter such regulations."
A lot of alterations occurred during and after the Civil War, with the 13th Amendment banning slavery, the 14th Amendment guaranteeing equal protection of the law and the 15th Amendment banning the exclusion of any person from the right to vote due to their race or "previous condition of servitude."
It took another 60 years to pass and ratify the 19th Amendment, the one that said that all states must allow women to vote – a development that happened roughly simultaneously with the founding of this august organization, created to help the newly enfranched half of the American body politic not only make use, but make informed use, of this most basic power of the individual.
In 1962, the 24th amendment, banning the poll tax, was ratified.
In 1971, as 18-year-olds were being sent off to Vietnam by a government they couldn't vote for, the states ratified the 26th Amendment, telling all states they could set the voting age no higher than 18.
Such amendments to the Constitution often contain the kicker "the congress shall have the power to enforce this article by appropriate legislation." In the case of the reconstruction amendments, appropriate legislation was something Congress did not fully get around to for basically a century, with the Civil Rights act of 1964 and the Voting Rights Act of 1965.
After that long line of successes, we have created a society where we are all required to at least pretend to support universal sufferage, as definied as all adult citizens, with some reasoned back and forth on such details as restoring the voting rights of convicted felons once they have served their time
or drilling into the details of the paperwork attendent to voter resistration
or concerns that the right to vote, sought for so long and as great sacrifice by so many, now seems valued by so few, at least as measured in voter turnout statistics, especially in so-called off-year elections, especially by younger people.
The big battles may seem to all be behind us.
The League of Women Voters, of course, continues. It works tirelessly to encourage people of both genders and all other descriptions to register and vote. And its mostly volunteer leaders and members engage in deep, reasoned, non-partisan research of important but complex issues so as to help female voters, as well as the other kind, to not only vote, but to vote intelligently.
This is useful work, obviously, as useful in an age when information bombards us from all directions as it was in an era when information traveled more slowly, by mail or by mysterious dots and dashes.
I would surmise that all of this devotion to active citizenship work rose from a day when the idea of women voting was something that a lot of people, of both genders, still had to get used to.