Well, the assassination wasn't a fluke, it wasn't a near run thing, it could not have gone the other way easily. The assassination of the Archduke Ferdinand stands in stark contrast. That barely happened, Caesar was pretty much doomed.
I don't think it's interesting to suppose he simply survived that attack.
So if we're supposing he was not assassinated we're supposing that the assassins, which is to say half the senate, decided not to assassinate him. So you have to start your speculations with why they made that choice.
If they just chickened out you could suppose that Caesar continued to amass power, and, when you add avoiding the civil war, you get a very powerful Roman Autocracy heading into the new millennium. Maybe you avoid the Second Century Crisis and all that rapid turnover of emperors that makes the Klingons look like pikers. The barbarians show up in the fourth century and Rome just squishes them and keeps growing.
If they decided to start the civil war early then you get a different civil war. Caesar is good at war, but he's going against one of Rome's fundamental values: no kings. So a lot of Consuls might get opportunistic and take the other side. Maybe Caesar gets killed and things proceed as we know them. Maybe Caesar wins, but he'd have to make a lot of deals so would not end up as powerful as he might.
Or maybe they find a way to solve the problem politically. They gather allies, suborn Caesar's allies, and conduct a political reform that restores something like the Republic.
If you produced a book by having a dozen top writers each put together a chapter on one possible alternate scenario, I would read that book.