Was the civil war inevitable? How might compromises have forestalled the division between the North and the South?

There is really no way to prove that any historical process or event was inevitable if we go back far in enough in the chain of events that preceded it and say that if events "a,b,c,d, and e" had not occurred, then f would not have had to happen. For instance, if we go back to the 1790s and hypothesize that the cotton gin had not been invented, then it is possible that the "need" for enslaved people would not have grown as it did (because of the need for more people to harvest cotton given the faster rate at which the machinery made it possible to process it) and the Southern leadership would therefore have had the sense to free the enslaved people, just as the Northern states gradually did during the same period. In that hypothetical case, there would then have been no sectional conflict, and hence no war.
However, 1793 was nearly seventy years before the country did blow up into warfare, and a huge number of events occurred between then and 1861 that cumulatively did place North and South into a state of irreversible conflict. One compromise after another was attempted during this period, with the intention of keeping the Union together, but each one either backfired, or other events occurred that exacerbated the sectional divide instead of ameliorating it. To mention just one such event, the Louisiana Purchase in 1803 added an enormous territory to the United States, including territory where slavery was already in practice and additional areas to which the slavery could be extended. At the time the Constitution was ratified nearly fifteen years before this, few people could have anticipated the US would so quickly be expanded this way. But once expansion became a reality, and was furthered with the land taken from Mexico in the 1840s, the slavery issue became even more inflammatory and impossible to resolve.
In my view, given the conditions that existed by the year 1815 when the War of 1812 was concluded, it would have been highly improbable for the sectional conflict to be defused by compromises of any kind. Something had to happen sooner or later, especially when one considers that the US, even at the time independence was secured in 1783, was already a huge geographic area stretching from Canada to Florida and from the Atlantic to the Mississippi. It had taken centuries for the geographically smaller Western European countries of Britain, France, and Spain to achieve territorial stability and unity. At the time the US was created, Germany and Italy had still not achieved unification and were not to accomplish this until 1870. That a central government could maintain its authority over the already vast territory of the US as it was in 1789, without eventual sectional warfare breaking out at some point in time, would have been nearly impossible.