I understand there would probably be a gap of a few years between the end of the war and the start of any big migrations of former slaves. Reconstruction did offer the prospect of things getting better after all. But once Reconstruction ended in the late 1870's I'm curious why the African-Americans endured Jim Crow for 30+ years before you see the Great Migration get underway.
The thing is, before the Great Migration there was already a large movement that tried to escape the violence and undemocratic government of the Jim Crow South, which took place in the late 1870's to the 1880's. A host of factors explain why this first exodus failed to move as many people as the Great Migration did.
First, for context, let's discuss what happened in the aftermath of the war. When the South was defeated the destruction of slavery was assured, but far from settling the question the emancipation of more than four million of human beings opened new contentious debates and challenges. This is what's called the Reconstruction Era. Long story short, originally Reconstruction operated under President Andrew Johnson, who assumed power after Lincoln was assassinated. A racist who had no interest in changing the way the South worked, Johnson nonetheless required them to accept emancipation as an inescapable fact of their defeat. Yet, Johnson allowed White Southerners to take charge of the new government, returned what little land had been confiscated, and denied freedmen the protection of the Federal Army. Despite the heroic efforts of the Freedmen's Bureau, most Black people were forced into a condition close to slavery by a series of "Black Codes", that limited their rights and tried to reestablish the plantation system.
During Presidential Reconstruction, Black people thus continued to suffer oppression in many ways. And in the face of this situation, thousands did migrate... to other parts of the South. Described by hostile observers as an "aimless migration", a "vagabondage", thousands of Black freedmen left their plantations and moved either to Southern cities or Western states like Texas, where wages were higher and the presence of the Bureau and the Union Army assured at least a modicum of protection. Southern cities, where "freedom was free-er", saw their Black population double in the aftermath of the war. Unfortunately, often Black people had to settle in "shantytowns" built in the periphery of the cities, resulting in precarious living conditions, disease and menial employment.
It's possible that the migration would continue and turn towards the North with time, but the start of "Radical" Reconstruction prevented this by giving Black people hope that things would turn for the better. Outraged at Johnson's actions, which seemed to surrender the South to the control of White Supremacist rebels and nullify the gains of the war, Republicans passed the Reconstruction Acts over his veto and started the process anew, further securing it by passing the 14th amendment. The new Republican regimes that appeared in the South were a radical departure from previous Southern governments, for they at least tried to assure equality before the law and extend the protection of the State, hitherto always denied, to Black people. Reconstruction also opened the way for Black officeholding and new economic opportunities, as having the law on their side allowed Black laborers to negotiate better terms of employment. Even when counterrevolutionary terrorism in the form of the Ku Klux Klan swept the region, Black people could count on the aid of Washington, where President Grant was committed to the defense of Black rights.
But Reconstruction collapsed. The reasons why are too complex, but at the end of the Grant administration a tired North, unable to summon the will or power to enforce the law and protect Black rights, simply gave up the fight. The election of 1876 traditionally marks the end of Reconstruction, but the sad fact is that it probably would have ended no matter what. Grant, though still sympathetic to Black people, had no effective strategy to deal with the question. Sometimes acting decisively, sometimes not so much, Grant found that no matter what he did he aroused the opposition of Northerners who were simple exhausted and wanted to move on. The Reconstruction states, corrupt, weak and broke as they were, collapsed under terrorist violence supported almost universally by Southern Whites. By 1877, all Southern states had been "redeemed", opening the way for White Southerners to reestablish White Supremacy and the oppression of Black Americans.
In the face of this outcome, the first Black exodus out of the South started. Reconstruction had been one of the few times in which the South offered opportunities to Black people, resulting instead in Black Northerners moving towards the region. But after 1877, interest in migration, "all but moribund during Reconstruction", revived. Several thousand expressed interest in migrating to Liberia, yet few did and many returned at the end. This was partly because of the financial exigencies of such a trip, but also because Black Americans simply didn't want to leave their country. So they looked to the West, hoping to settle in the Federal territories or even asking Congress to create a territory explicitly for Black settlement. Kansas was the main destiny for Black immigrants, who, however, didn't find the land and employment they wanted, but often had to settle for menial labor in the cities. Still, it did allow them to escape the violence of a South that was moving towards reinforcing White Supremacy by wiping away the last vestiges of Reconstruction.
Some 21,000 "Exodusters" moved out of the South and mostly towards Kansas in 1879-1880, hoping that sympathetic Northerners would bring them aid. Unfortunately, Northerners mostly offered moral support. Observing that African Americans were leaving a Southern conditions "only too strongly like those which have driven many a foreigner across the seas, to seek in our land the liberty to labor for himself and his family", they talked positively of Black emigration, with a newspaper saying that Black people were just looking for "peace, law and order, the security of property, the rights of man, and a chance to better their state." This immigration, the New York Times concluded, would continue as long as "the laborer, white or black, is oppressed. While labor is considered servile, and the condition of the laborer made irksome, there will be discontent and flight.”
P.B.S. Pinchback reported soon that "the exodus has assumed alarming proportions, which threatens to depopulate the State of her laborers", to the point that some apparently were looking into "importing" Chinese workers. This "revolt of labor", Northerners observed gleefully, would weaken the South and force the White population to come to its senses and offer better treatment to Black laborers. But initial support crumbled when a group of Black people migrated to Indiana. Democrats said Republicans were encouraging the migration simply to win Northern states, by importing enough Black voters to supply their deficits. Republicans then said that Black Exodusters were simply laborers who, having seen their rights denied, sought better conditions. But the Committee that met to examine the exodus to Indiana produced a report that, in the words of historian Heather Cox Richardson, conciliated these visions. A parade of witnesses, including well to do Black professionals, testified that Exodusters were "the most ignorant of the country people", "the floating class" that just didn't want to work and believed that by migrating they would get everything for free, while the intelligent and laboring could succeed in the South.
This aligned well with Southern claims that Black rights were, in fact, respected and that social mobility existed. Alarmed at "communism" in the North and afraid that they had been actually helping lazy vagrants, Northerners stopped their support. This view was reinforced by that of thinkers such as Booker T. Washington, who insisted that by shunning politics and focusing on education Black people could achieve success. At the end, less than 50,000 people ever left the South during this first exodus, meaning that for all its political importance the demographic impact was minimal. This was owed to the fact that opportunities outside the South weren't much better, that migrating was very difficult, but above all that Black rights hadn't been completely destroyed yet. In some areas there still remained Black officeholders and voters, and despite violence Black laborers were still able to strike and demand better conditions. The Northern economy was still depressed, while conversely Southern plantations required labor, resulting in relatively good wages even if good treatment was lacking. The South had to furthermore still tread lightly, for it was possible that being imprudent could reawake Northern anger and rekindle the conflict over Reconstruction.
The consolidation of Jim Crow and segregation thus took place in the 1890's, where the great majority of these vile provisions were enacted. Violence took a turn for the worse then, resulting in the "nadir of race relations", where lynchings and other forms of terror became even more common. Whereas Black people still had some hope that they could build a living, or that Reconstruction could return, now they lost it completely. This was joined by the fact that Northern factories urgently needed laborers, resulting in much greater support for migration. The structures of the Black community, by then fully established, also helped in this movement. Moreover, with their rule and economy stabilized, White Southerners now didn't oppose that exodus, whereas before they had apparently held Black laborers back at gunpoint. Though The Great Migration started in the 1890's with the migration of Black youth to Northern cities, the movement started in earnest in the period from 1910 to 1930, where 1.5 million African Americans left for the North. Altogether, several factors converged just right in that period, factors that hadn't been there during the first exodus in the 1870's. Nonetheless, the rhethoric and memory of the "Exodusters" did help to inspire and shape the Great Migration.