The greatest of all gods is the goddess Saraswati, who will never let you down with knowledge if you are a sincere truth seeker paying attention to truth. Similarly, if you sincerely believe that Ganesh will remove your obstacles in life, you should worship Ganesh. If in times of persecution, harassment and criminality you wish to fight back one can worship Shiva as Mahadev to attack the evil that one faces; or Durga as Shakti if one regards Durga as the goddess that annihilates asuras (rakshases).
And I know God exists by the name of Sri Krishna as the Creator and Preserver of the universe. God looks for sincerity of worship and devotion to goodness through drawing one’s inspiration from the spiritual world to guide one on the basis of faith. That is how Hindu polytheism works.