Working at a big company is not necessary or useful experience for creating a successful startup, and starting a tech startup now is possible regardless of lack of problems, savings, or blue chip tech experience.
Trying to gain experience by working for a big company often leads to increased spending and slower learning, ultimately hindering the creation of a successful start-up.
Start building your tech startup even if you don't have a problem to solve, money in savings, or a blue chip tech company on your resume, as these are not required to get into YC or be a successful founder.