If I'm reading it right, on both hands where your thumb is, use your thumb to hit the F and G natural that fall closest to it.
F3 and G3 for the left thumb, and F5 amd G5 for your right thumb. Once you do that it'll free up your other fingers for the other notes. However, it is still a very wierd stretch, and if you're not used to it, IT WILL HURT...
I play and I can tell you, when you're not used to the stretch, it takes a moment before it'll feel comfortable.
Side note: I almost didn't know what the *WARK* to do. When I first looked at it I thought, that's only possible by rolling your fingers across. Then I said, "No, no.......No, no....Wait, wait...."
Good luck, seems like a challenging piece.....challenging.........but fun....