Where did you get that number? Wikipedia says this:
One study found that there were "4,467 total victims of lynching from 1883 to 1941. Of these victims, 4,027 were men, 99 were women, and 341 were of unidentified gender (although likely male); 3,265 were black, 1,082 were white, 71 were Mexican or of Mexican descent, 38 were American Indian, 10 were Chinese, and 1 was Japanese."
So I assume you saw that number quoted for all American history when it was for about 60 years, according to this one study.
This was the lynching period. Everything I've ever seen indicates lynchings, like many crimes*, were mostly negligible before that period. Lynchings always have happened but it was after the Civil War as Jim Crow came into being that it became a practice because the law, especially the ostensible equal treatment of the races, was seen as deficient to dole out justice. The police were often complicit because judges were seen as too beholden to the law (or worse being struck down by higher courts) and the process of even unfair trials would find people not guilty and wouldn't sentence the "criminals" to death immediately. In any case this wouldn't be "countless thousands" in the 20th Century alone being falsely accused by white women because we don't even have 5000 recorded victims.
*This is important because lynchings were usually not spontaneous and random acts of chaos.
edit: Let me be more specific about the timeline and why lynchings became a national concern. We know of
individual lynchings before the Civil War, but lynchings were not a practice or systematic as they became in the Jim Crow South and we shouldn't expect them before the Civil War targeting free Blacks because in the South most Blacks were slaves and generally slaves did not get access to the normal justice system anyway especially so after Dred Scott. (You usually couldn't form up a mob and dole out vigilante justice against someone's slave for just anything, this would be violating their property and the slave owners would definitely have you punished. If a slave committed a crime it was typically incumbent on their owner to make the other person whole, correspondingly the owners had to "police their own" rather than lose the slave to the free justice system*.) IIRC, most of the comparatively fewer Northern lynchings across the entire American period were recorded as religion-based although we would now see that as also suggesting an ethnic component like with say, the Irish or Italians or Jews.
*This is what makes people think there's a kernel of truth in the Southern mythology, that Blacks were "better behaved" and better off under slavery. The idea of a criminal presupposes a normal good citizen, slaves were not thought of to have this capacity as they were property. Follow this line of logic and you can see why nobody wrote about "Black criminality" in the antebellum South. (This line of thought was enticing to everyone who lived through the changes, and beyond, because they were comparing the
entire population (of all races) to the reputation in the South of
free Blacks who were always abnormal individuals or the probability they would have escaped and stayed out of slavery in the first place would have been low. The free Blacks (as a population) never provoked the creation of segregation in the South because the rare free Black sitting on a train or whatever wasn't offensive as it became because you
knew he was a "good" one since he wasn't a slave, this wasn't the case in the North which is why Northern states did things like make it illegal for a Black person to come in the state at all.)
