Disclaimer: I have never worked for a Big 4 company, and the only interviews I had with them were during college with Amazon, and I've failed both of those, either in the 1st or the 2nd round. So I'm not a success story. That being said, if I were to set this as a goal, I know what I would do.
> Is it possible for someone to not be cut out for software engineering?
The answer to such a question is always 'yes'. But there's a lot of danger in assuming that you are the someone. This is betting against yourself. And there's only one of you in the current reality state. Don't bet against yourself. That is not how you should think.
Definitely don't bet yourself in this instance if you already have experience successfully getting multiple jobs...
What you should investigate instead is what do you want, and how much you want it. Consider the various pros and cons and how they make sense to you. How much do you really want to work for a Big 4 company? How do you feel about some of the potential tradeoffs (i.e., time spent on learning algorithms and interview questions)? Same with the software engineer question. How much do you want to be one? Why? What are the tradeoffs?
[Note: not all tradeoffs are "true" tradeoffs, i.e., that you'll loose something. Learning algorithms may make your mind sharper and help you in other areas. But it also means you can't spend that time on, say, relationships, entertainment/hobby, or even something in the health department. There's nothing wrong with tradeoffs and don't scrutinize them too much but still be aware that nothing you do is free]
The problem with the question of "am I not cut out to be a software engineer / Big 4 employee" is that no one can answer it, including you. You will, most likely, never ever know unless you reach some success point where you can definitively say yes. You can't just base it on things like being rejected by many companies or struggling in college, because that already implies those are reliable proxies and that's a really shaky assumption. I had trouble in college, too. I graduated with a 3.0. It doesn't seem to mean a thing, other than what it literally means.
> So far, I have interviewed for and been rejected by no less than 10 different roles. I was also rejected by approximately 20 companies during college. I always fail during tech portions.
This is neither here nor there. There are a lot of factors that could go into something like this, it could be way too many things. Not enough information. The only thing I'll say is try to develop a model of what kind of companies you are not a good fit for, so that you don't spend too much time on them, and avoid wasting too much time on unlikely pathways unless you really want to work for some specific companies. I would often apply to very few places, get offers from all of them, and then choose among that. Applying to lots of companies indiscriminately was both stressful and yielded nothing. Also, don't be discouraged from applying to places that have requirements you don't meet but are nonetheless interesting to you.
Also, field, location, frameworks, what the company lacks, how the company is doing, etc., all affect your chances.
> performance anxiety
I got rid of my performance anxiety mostly through a major philosophical shift. I don't know if this is a topic that one can give "simple" advice on... in the context of interviews, for any given interview, assume that you will pass it. Just assume this, without making anything depend on it being true. Any time something in the interview goes "wrong", just assume it doesn't matter. Don't think about how you "should" know the answer to some question, just give your best answer or say you don't know and move on and do not assume that this jeopardizes your interview.
Whether you did something "wrong" during the interview, you can figure that after it is over. And, remember, they're just interviews. You do not owe to the world to pass them, they don't say something insidious about you, you're not a worse person for not passing one, nor are you a worse software developer for not passing them. You interviewing for your benefit, not theirs or anyone else's.
> If my goal isn't an impossibility, how can I efficiently progress towards it? Would a mentor be helpful?
Assuming you do decide that getting into a Big 4 company is a fairly high priority goal for you (and, really, even if it's not), the first thing I would recommend is making sure that you're focusing about progress and results as opposed to time or work. You want the most productive results from the least amount of time and work. All work should be justified.
Essentially, you're trying to learn how to solve algorithms quickly and under pressure. As with any learning tasks, this is a fairly big and complex topic that's not well understood. This is where you want to apply your learning how to learn skills and try to pool whatever intelligence, intuition, and knowledge you currently possess. I can write, well, a lot on this topic so I'll try to keep it relatively short: try to figure out what is needed and what is missing in your head, and try to find a way to process your learning style and what kind of things give you trouble. Grinding on a problem over and over actually probably benefits more brilliant people more than the slow ones among us, since the brilliant people can make their brain form all the connections, we actually need to trace what goes where.
Maybe you have a poor memory and you need to organize the algorithms you're learning. Maybe you're not used to writing code a certain way and you need to do that. Maybe you should take a stab at some weird language to free up your brain from misconceptions. Maybe you should play a video game to see some pattern you've never paid attention to before. Maybe you should get some sleep and stop worrying about things for a week. It's a bit of a strange process at times but it's not entirely hit or miss and if you are very attentive to your brain and you do not waste time shaming and guilting yourself, you can discover a lot of interesting things about how you work, whether or not you'll make it into that Big 4 company.
I can write more about this but it's not going to fit in an HN post.
Just, don't bet against yourself.