Hi,
once you have selected the profile you like for navigation (i.e. car, bike, etc.), try checking:
[OsmAnd Menu] -> Configure profile -> General settings -> Display position always in center
With this, you can choose whether the map will follow the display center (option enabled) or bottom (disabled)
In order to make the map auto-follow your current position, just look at the button in the bottom-right of the display (a small circle with crosshairs): if it's blue-background and white crosshairs, then the map will stay centered on the view you manually set.
Just tap it, and: it will become white-background with blue crosshairs and the map will automatically follow your current position (provided you enabled Location Services and your device is properly receiving GNSS signal).
Best regards,
Max