That's right as far as our physical being is concerned, but, He has given us a free will, and, when we exercise it in a way that is not pleasing to Him, we can expect to suffer the punishment of that transgression.
Throughout time, God has sent Prophets and Messengers to people in all regions of the world in order to teach them the Laws that we should abide by, in order to maintain peace among ourselves. God, being our creator knows our nature better than we know it ourselves, so, by following what He has revealed to us, we can save ourselves from a lot of strife.
The Revelations that were revealed to man by God are akin to instruction manuals. They all basically say the same thing but, throughout time, there have been certain interest groups that didn't appreciate the Revelation, for various reasons, and sought to kill the Messengers and to change the Message to suit themselves.
The Muslims believe that the Qur'an is the final Revelation from God. In it, all the Prophets of old are mentioned, including Jesus (May peace be upon all of them). There is even a chapter named after Jesus' Mother, whom we hold in very high esteem.
Did you know that the word Muslim means 'someone who submits to the Will of God'? And the word Islam, is derived from the word salaam (peace) and is best translated as meaning 'the way to peace through submission to the Will of God'.
In light of that, we consider all the Prophets, including Jesus, to be Muslims.