Agreed. I've never had much difficulty finding software development work at smaller companies. If I have the required skills that they are looking for, I'm usually confident that I'll get an interview. An interview at a smaller company is likely to be much shorter and easier than the algorithm-based interviews at larger companies. The chance of an offer is also much higher.

The pay at smaller companies is still good enough for you to live comfortably, even at the entry-level. I worked a software development internship half-time while going to college, and it was easier and more enjoyable than all of the non-programming jobs that I did before that.

If you can't get a job at the companies that you want, you have no choice but to settle for something else until you have the experience and knowledge that is required.

Thinking some more on it, there is another (long shot) way to get hired at a large company: start your own software company that is eventually acquired by a large company.