Can I get full custody of my child born in Japan?

All cases are fact sensitive. It appears your wife is a US citizen living on a US Military base in Japan and that the child has not been born yet.  It does not appear that she is a Japanese citizen.     Jurisdiction over the child will likely be in the place where the child is living.  If the child is born and remains on Japanese soil, Japan may technically have jurisdiction to make decisions.  Japan has custody (legal decision making), parenting time, and support laws that are applied in these cases. As of January, 2014, Japan finally joined the Hague Convention which, briefly, is an agreement of many countries intended to stop cross border child custody matters.  Prior to that, I was already seeing some cases where the Japanese court and Japanese attorneys were recognizing the importance of both parents having appropriate parental access.  If mom is in the US Military, is it likely she will be sent back to the US?  Further, the US Military does have resources that may be of assistance when a service member attempts to deny the other parent access.  There may be some benefits to getting your divorce filed in the United States now and getting Mother served.