I’ve always thought Lee’s reputation was very fortunate in his selection of opposing generals. I can’t remember the exact quote, but I think Lee knew the game was up when Grant didn’t retreat after The Wilderness.
Grant hated delay. He knew it also gave his enemy time to plan and regroup, and felt that he never gave him an advantage. Whereas, pressing forward with whatever he had usually did give him an advantage, because the enemy didn’t expect it.
As far as the Wilderness goes, Grant knew he had the numerical advantage and that a draw was just as good as a victory. He also knew that he wouldn’t be turning back and that he would do whatever it took to see his pursuit of Lee through to its conclusion.