No, this is a misrepresentation. Most men didn't have the right to vote either, just the landowners. If you look at when men got universal suffrage, and when women did, that's often close together. And then we're not even speaking of black men and women.
"By 1776 at least 60 percent of adult white males were able to vote, and the proportion expanded significantly by 1787"
So most white men could vote since the country was founded.
Property qualifications were then steadily dropped (and never added for white men):
"The 1828 presidential election was the first in which non-property-holding white males could vote in the vast majority of states"
"The last state to abolish property qualification was North Carolina in 1856."
Do you consider the civil rights movement "close together" with now? Because that's the same amount of time it was between all men getting the right to vote and women being given the right to vote.