Was the Passover Always a Lamb?

The apostle Paul said that Christ was our Passover and he is referred to in the New Testament as the lamb. Was the Passover sacrifice always to be a lamb?
 

The ideal Passover animal that the Israelites consumed each Passover at Jerusalem was a lamb, and that is what most people sacrificed. But, (and many people are surprised at this), the goat was equally acceptable (Exodus 12:5).

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