How to know if you're not smart enough to be a great programmer?

I'm at a crossroads where I'm considering whether I should give up trying to be a programmer, specifically, a programmer worthy of a Big 4 job. I've been struggling daily with doing even leetcode/CTCI questions, not being able to implement even brute force solutions to relatively simple problems. It's been a month since I've been doing problems daily, but I've been trying my luck at tech problems on and off for about a year with dismal results.

I've asked people about this before and often people defer to a lack of experience, but that seems to be an untestable hypothesis. A person can always use more experience. What I would like to know is how can a person know when experience is not the issue. How and when can someone objectively know if the reason they are struggling/failing is innate intelligence? What are the differences between struggling because programming is difficult and one doesn't have enough experience and it being definitely being an issue of intelligence? At what point does a person have reasonable certainty that their time would better be spent pursuing something else?

Does a square peg fit in a round hole? The obvious answer is no, the circumspective answer is it depends on the diameter of the hole, the "can do" answer is: pass me a hammer. Should the operation fail, the "politically correct" response to the client will be 'we needed a bigger hammer' than specified in the initial project plan...herein is our revised project estimate...

Scrutinize the aforementioned gedenkan thoroughly. Rinse & repeat. Accidenture [decode it] and plenty of projects under execution by Deloitte, PwC, KPMG, Capgemini/E&Y operate just like this on a regular basis

Similarly, so are you {square peg in round hole) if you think solving a cicada challenge provides a hypothetic-deductive 'proof' of likelihood of 'worthiness' at any firm.

Conversely, if you cannot suss out the meaning of what has been provided in the previous two paragraphs, then it is indeed probable that certain "problem solving" requisite skills are presently absent from your internalized paradigms and personal processes...these can be learned and are not untestable...get a full-time gig and "just do it" as the Nike slogan alludes.

Best regards

I've wondered the same about myself. What I've come to about it is that there are definitely different types of programmers, and I have found what type I am and what makes me unique. Also I've come to that I may not always program just to program. I have higher goals that could use programming as a means, and for my specific goals I don't need to be the best. A good example is Pieter Levels [1]. He is not the best programmer, but he makes a lot of amazing (and revenue generating) things.

[1] https://mobile.twitter.com/levelsio