if you want to jump through the interviewing hoop at a major software/tech company make sure you grind through a basic entry-level computer science algorithms course.
where i went to univerity (in australia) this would be something like "algorithms 1" as a second year course for students focusing on computer science or software engineering. you want to come out of it with a decent understanding of how to implement and when to use basic data structures (not that you should ever need to implement them in the real world, but its good to understand the fundamentals) and an ability to do informal (i.e. not formal mathematical proof) asymptotic analysis ("big oh" notation) for time and space complexity of algorithms. (on the other hand, if you ever took some math courses and soaked up epsilon delta or epsilon N formal definitions of limits, then you might enjoy the formal definition of big-oh stuff, but i dont imagine anyone is ever going to ask for a formal proof for a hands-on software dev/eng interview)
apart from some knowledge or intuition of when to use which data structure, which you probably need to use every day, you dont need to use the above in most actual industry software dev roles, but it does tend to get measured in software engineering interviews.
there's a reasonable amount of advice over in this thread -- look for the comments from people who have experience interviewing for the big K (for small finite K > 1): https://news.ycombinator.com/item?id=17755688
A completely different angle is not to focus on the big tech companies, and instead focus on tech roles in large non-tech orgs, or delivering value to businesses that happens to be partially implemented using technology. there tends to be a much lower bar to entry in terms of needing to clear hoop-jumping technical interview processes (for better and for worse).