Some teacher from your past probably drilled you about not starting sentences with because until you started having nightmares about it. We're here to tell you that it's totally fine. Take that, Teacher from Your Past.
You just need to be careful that, in formal writing (like essays for school), you don't end up writing a fragment like Because he hated to shiver.
This clause is dependent since it starts with because, a subordinating conjunction—that means that on its own, it's a fragment. Other examples of this part of speech include when, unless, although, and the list goes on.
As long as you follow up the dependent clause with a main clause, your sentence will be complete. Oh, and don't forget your comma.
Example
Because Julian left his mittens on the train.
OR
Because he believed the water was too cold upstream, Sammy the salmon did not want to migrate with the rest of the school.
Which sentence that starts with because has the right stuff? It's the second one. In that example, a comma is used to link the dependent clause Because he believed the water was too cold upstream to the independent clause that follows it, thus making a real humdinger of a complete sentence.
The first sentence is incorrect because it's a dependent clause left all by its lonesome. On its own like that, it's a fragment. If the sentence that came before it was "Why?" it might make more sense—but leave those kinds of fragments to Shmoop and informal emails.