That is a fascinating topic to discuss that of course could never be answered definitively. It also can be a tough topic to discuss due to the politicization of the topic that has existed since at least Appomattox Courthouse. If I had to sum up my opinion on this in a tldr it would be: Probably not, but stranger things have happened.

One of the more illuminating books I've read on this topic is, A Savage War, by Hsieh and Murray. A fairly recent single volume history of the Civil War that in part wrestles with that question. If I had to sum up their view, it would be that while the South was a large underdog by almost any metric, the task before the North, politically, militarily, economically, and culturally, was enormous and its result was not a foregone conclusion.

As for the North's advantages: It's economy was several times larger than the South's, as was its population. Not only was its economy much larger, it was more diverse. With well known advantages in technology and manufacturing, but also the Midwest was starting to boom as a producer of agricultural goods which helped to make up for the loss of the South's agricultural production during the war. The South's economy of course was very much dependent on cotton exports, which were not possible due to the Union blockade, and was much less built up in manufacturing in an era that arguably was the dawn of industrialized warfare.

This gets to another advantage of the Union which doesn't get enough attention, its overwhelming naval might. The South fought for most of the war under a blockade that stretched from the coast of Virginia to Texas, and from New Orleans to eventually the length of the entire Mississippi. The South had zero ability to materially impact the Union navy and the result was devastating on their chances. The North's naval control of the seas and the waterways gave it a huge logistical advantage over the South.

And yet while the North had enormous advantages over the South, they also had a much harder job. The South essentially needed to maintain the status quo after secession, the North needed to conquer an enormous and in many areas wild country full of people who were dedicated to fighting them. Murray and Hsieh make the interesting point that the distance from New Orleans to Richmond was roughly the same distance from Berlin to Moscow. The area the North had to conquer, hold, and pacify was of continental proportions and was a massive task for an army that just a few years before was not much more than a glorified garrison force.

Murray and Hsieh then stumble into the great man debate of history, in giving Lincoln and Grant enormous credit for the North winning the Civil War. Personally I think they make a good case. I think if the North's president had been a mediocrity, or there was no General Grant, that it's possible that the South could have held out for a peace deal and recognition of its independence. That being said, that's the only way I could see it happening. More through Union incompetence than by anything the South could have done differently.

Edit: Wow, thanks for the awards!

In addition to u/MaterialCarrot's excellent answer, I would also call your attention to the possible effects that slavery had on the war's outcome. Depending on your perspective, the institution of slavery was either an enormous boon to the Confederacy which allowed it to stand a much stronger chance against the Union, or it was a millstone around the Confederacy's neck which guaranteed its defeat. I tend toward the latter opinion.

On the plus side, slavery freed a large percentage of the Southern population from farm and manual labor. In the South, enslaved people performed much of the manual labor which would have been done by free men in the Union. Thus, the Confederacy could mobilize a significantly higher percentage of its population into military service than the Union. Although the total population of military-age white males in the Confederacy was less than 1/3 that of the Union, the Confederacy could put almost its entire male population into military service. This meant that the Union never had an overwhelming advantage in manpower, despite its much larger population.

On the negative side, slavery meant that the Confederacy was home to--and dependent on--a large population of people who were held under subjugation and actively hostile to the Confederate cause. This was a massive weakness which the Union exploited throughout the war in various ways. At the beginning of the Civil War, any enslaved person who escaped behind Union lines was classified as "contraband of war" and not returned. Later, this policy was formalized by the Emancipation Proclamation, which was meant more as a war measure to deprive the Confederacy of a valuable resource rather than as a humanitarian measure to free people. Every former slave who ran away and crossed to Union lines was one less pair of hands to harvest the crops or sew the blankets or dig the trenches which the Confederate Army needed.

Interestingly, it has been argued recently by Robert L O'Connell that enslaved people played an underappreciated role in the Union's victory by acting as informal guides, scouts, spies, and informants for the Union Army. Particularly, O'Connell zeroes in on Sherman's successful campaign through Georgia and the Carolinas, which broke the back of the Confederacy and probably did more to win the war than any other land action. Sherman's army marched more than 500 miles through hostile territory without food or good maps. At the time, Sherman's campaign was thought to be suicidal. However, it was a complete success, largely because Sherman constantly received information from enslaved people who despised the Confederates and wanted to see the Union win. If not for their assistance, it is probable that Shermans' March could have ended very differently.

Hello, it seems this question has been asked before:
https://www.reddit.com/r/AskHistorians/comments/1e1oa5/civil_war_usa_did_the_south_ever_have_a_chance_to/

The US Civil War was never about outright victory for either side to be perfectly honest, although the North certainly could have. The problem with Civil Wars in general is the winning side will have a lot more work to do if it obliterates the loser. Since you know, future of the country and all that. The North and Lincoln's objective was to stop the insurrection. They won because of a few serious losses by the Confederacy coupled with a bit of starving them out. On the other hand, what if Johnston and Stonewall don't die because of friendly fire or perhaps even more of an alternate if Stonewall is allowed to pursuit after Bull Run onto Washington is such an early period of the war before Lincoln's call for half a million troops? It gets very political. Other considerations would be if Kentucky & Missouri join the Confederacy in more than half or at least serve as more supply and buffer benefits. I think it's because of these nuances many from the South may believe the Confederacy definitely had a chance. I haven't even discussed European involvement which frankly put if the war extends by even a year may have come to pass or just if things are in more of a stalemate prior to the 64 election. Imagine a bunch more Cold Harbors in the best case scenario. Now McClellan lost by a wife margin in the electoral college to Lincoln but New York was by less than 1% and several others were within 5%. If the Confederacy does quite a bit better including Gettysburg it's entirely possible he loses that election. Historically he was the first President since Andrew Johnson three decades prior to win re-election.

So then we discuss how a Confederacy "win" looks like. It's basically status quo with slavery obviously but the Confederate States rejoin the Union as well if not at the end of the war then later. I just don't see the same outcome is all I'm saying. Definitely no reconstruction, but the economy of the Confederacy is an interesting variable. Their money wasn't backed by anything tangible so suffice to say economically there would be a lot of interest in rejoining the North in one way or another.