You've asked a very good question and a very complex question. Jurisdiction issues are unresolved by Florida's courts, and these issues are being hotly litigated. All I can tell you is to hire a lawyer, and yes, that lawyer should certainly file a motion to dismiss for lack of jurisdiction. I agree with you that's it's impossible to have 50/50 custody when you live an entire continent apart, but you may be able to have shared parental responsibility, which is the ability of the two of you to parent your child together, deciding together how your child is to be raised.
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Your question is complex.Technically, your child does not have a home state. Home state is defined as the state that was the residence of the child before the petition was filed. Since your child is one month old, a Florida court may exercise jurisdiction if it determines Florida is a convenient forum. The fact that father lives in Florida and an action has already commenced, WA may decline jurisdiction. This issue is complex. Please consult with an attorney asap.
While the UCCJEA may mean that the home state of the child is Washington, the child's father could make an argument that, because you both lived in Florida, the child was conceived in Florida and you just recently moved to Washington, permanent jurisidiction lies in Florida.
Rather than file a motion to dismiss for lack of jurisdiction, you might strongly consider filing your own custody motion in Washington first. Before you do anything, you need to visit with an attorney in your area in Washington who has a practice focus in family law, particularly child custody. This is too complicated an issue for you to handle on your own.
Also, a word of caution. Regardless of what happens in these initial stages, you will not subvert the rights of the child and father to parenting time forever. You need to start thinking now about how you will navigate the next 18 years.