I want my character to walk fast then over a few seconds of walking to run and then after a few more seconds to sprint. So to accelerate without a button, just overtime. A bit like Okami or Nier Automata.
In the CharacterMovement section of your Character Blueprint you will find the MaxAcceleration setting and the MaxWalkSpeed. Play around with these until you get the desired behaviour, e.g MaxAcceleration = 1000, MaxWalkSpeed = 2000. You can then also play different running animations based on the current speed of the character.