Just because he isn't Force sensitive, therefore can't use the Force, doesn't mean that the Force can't move through him. When he chants his mantra, he is literally trying to open himself to the Force and trusting that it would let him get what he needed to get done. Legends material showed that Jedi training is mostly mundane: intense physical training, meditation exercises, emotional stability exercises, etc. It isn't explicitly said in TCW, Rebels, and the films what the training regimen is but there are examples of mundane training enhancing their ability to use the Force. Obi-wan telling Anakin to calm himself and take a breath before going into the bar. Luke trying to enter a meditative state while hanging upside down in the wampa cave. These are all things that real live humans in the real world can do.
By making himself receptive, maybe, just maybe, the Force might be able to tell him something useful.