Obviously, you can't beat them, no matter how hard you try.
You can spend your entire life trying to beat these guys and never succeed at that.
But the important question here is: do you HAVE to beat them?
I can only speak from my own experience and I can tell you that every time I am doing a Google search and there are huge authority sites on top of the results, I just skip them, and move down the results to smaller sites that are more focused on the search term that interests me. I believe that many other people do that too.
So, is it 100% important to have the #1 spot on Google when the sites above you are the giants in that niche?
Do you know of any cases where not being in the Top 5 on Google didn't play a huge role in terms of getting the traffic you expected because people skipped the big ones and scrolled down to he more focused results?