Using a limit was extremely difficult to conceive. The Greeks and others were doing very well with geometry even 200 BC. The concept of the limit, which is the basis for the calculus, was conceived by Issac Newton in the mid 1600ths. So from the time of the Greeks to Isaac Newton it took around 800 years to conceive of the limit. That is why it is hard to comprehend at first. Even the greatest mathematical minds for many many generations could not conceive of this thing called the limit.
What finally helped me understand the limit is reading about trigonometric and geometric applications of the concept, as well as engineering applications. Also, there’s a number of mathematical discussions about it in various places. I guess it just finally sunk in, because one day it just seemed obvious as it’s own “thing” and I found I’d accepted it. So yeah, you’re right, for me at least it was just a paradoxically simple concept that I could not wrap my brain pan around no matter how I tried, except finally from sheer familiarity over time. That was the first time I ever faced such a conceptual difficulty, and it threw me for a very long time. In contrast, imaginary numbers were SO impossible to imagine I just accepted them as defined and never struggled with them. So maybe it boiled down to my belief I could somehow actually imagine infinity, and that was what I kept trying and failing to do.