The north had many more practical advantages over the south. The had more industry which could provide for many of their needs. Because of a stronger economy, they also had the financial resources to sustain themselves during the war. They had leaders who seemed significantly stronger in tactical procedures. Had the war, continued for years and years, these things might have eventually lossed their power.
I am not sure that it was inevitable that the North would win the civil war. However I would think it was definitely the favorite from the beginning. It had the industrialization to produce what it needed to fight the war, however the South had the natural resources.
I can think of two senarios by which the South might have won. 1) If it had inflicted a crushing defeat on the Northern army early in the war. 2) If it had turned to guerilla warfare and thereby so prolongued the war as to wear out the patience of the Northern people. There was no way the South could win a long, conventional war, becausethe industrial capacity or the reserves of manpower were so much greater in the North than in the South.
In the words of Shelby Foote, considered America's pre-eminent Civil War historian and contributor to Ken Burns PBS series Civil War, "The South never had a chance in that war". I tend to agree.
The South was outnumbered four and a half to one in white population, outproduced four to one in industry, had only one tenth of the nation's railroads and started the war with no navy at all. Those are long odds.
The best chance the South had to win the Civil War was to win foreign recognition and support from Great Britain. If they had entered the war on the Southern side (and they did seriously consider it - going so far as to build warships for the South in British shipyards) they could have broken the Union naval blockade, bought southern cotton, sold them arms and sent troops to fight alongside the confederates. Once Lee was defeated at Gettysburg, there was no other chance for this to happen, and the South would inevitably lose the Civil War.
(Also: You state in your question "During the time African slaves transported to America". The importation of slaves to the US ended in 1808, by Constitutional law. Slavery was still legal, as was their purchase or sale, but not their import.)
The greatest lesson of history is not just having the answer...but the why and how from the answer. The answer to your question is yes, it was inevitable the north would win the war. What is interesting is that the south won more battles than the north, yet the north won the war. From an historical perspective the south might have had the will but because they were economically dependent upon the north it was only a matter of time. The Confederate south became an increasingly depraved situation.
This is why;
1. Even though the north lost battles, the army maintained its resolve
2. military organization, hierarchy counts
3. had the capacity to manufacture all goods and services necessary
4. money...the U.S.Federal Government had it, the Confederate Government never measured up
5. the uncompromised leadership of President Lincoln
I do not think that the results of things like wars can ever be truly inevitable unless the two sides are just so badly matched that there is no way one side can defeat the other. In the case of the US Civil War, the two sides were not so badly matched as that.
For sure, the North had many advantages. It was much richer and had much more industrial capacity and many more men who were eligible to fight. But it also had things going against it. The main one of these is that it would have to completely defeat the South to win the war. The South, by contrast, only had to hold on long enough to make the North give up.
There were many points during the war when it seemed the South might win. This says to me that the sides were pretty closely matched and the war could have gone either way.
Speaking from hindsight it is easy to say that the South never had a chance to win the war, although they did win a few very important battles. To quote the renowned historian of the Civil War Shelby Dade Foote Jr.,
"I think that the North fought that war with one hand behind its back...If there had been more Southern victories, and a lot more, the North simply would have brought that other hand out from behind its back. I don't think the South ever had a chance to win that War."
The reasons why the North won the war was it had a larger white population, better industrial capacity and most importantly they had the money to support the war with machinery and ammunition. Above everything else they had a remarkable leader in Abraham Lincoln who chose sagacious generals like Grant and Sherman who tactically proved too much for the southern armies.
The positions or strengths of the two opposing groups just before or upon beginning of the American Civil War was not such that a conclusion could be drawn that the course of war and the success of North could have been predicted accurately. There were many twists and turns in the course of war in favour of one or the other sides, before the final results came. As a matter of fact, some experts believe that at the time of the famous Gettysburg address by Lincoln, the people in the North were becoming weary of the war and perhaps wanted to end it.
However we can say one thing that ultimately the practice of slavery would have ended in USA, as it has ended in the rest of the world. This is not because humans have become more kind and considerate towards, but because, it has been established that under the present economic system based on sophisticated technology, free manpower is more productive and economical than slave labour.