I think you pretty much answered your own problem. yes I think it is time to take up the alpha roll as soon as possible. Unless you do this problems will only get worse and he could end up hurting someone. He has to learn that all members of the family, including the baby, are above him - it will take some time at first but dogs most dogs take to it pretty quickly.
I find that most dogs don't like being alpha dog, it's a very stressful position and most dogs give it up quite easily, it's almost as if it's a relief not to be top dog. with the more powerful dominant breeds this is a little harder as you constantly have to be top dog 24/7 as may will challenge consistently.
When a dog enters a family, if there is no clear leader, the dog has no choice but to adopt the role of alpha dog, it's their instinct, not a choice.
Good luck
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