Process to adopt Japanese step-child

I (US citizen) married my wife (Japanese citizen). My wife has a kid (Japanese citizen) from a prior marriage (Japanese ex husband). We have since moved from Japan and now live in the US for a couple of years now. Both my wife and son have green cards. I am now trying to adopt my son. US law requires consent of both biological parents in order for the step father to adopt. The ex husband has not been in contact with my wife or son for over 8 years. How would we contact the ex husband if we don't even know where he is or if he is even alive? why would we need his consent if he practically abandoned them.

I'm in somewhat the same situation but this doesn't affect the Japanese law at this point.
You can contact the legal offices in the US to get a better picture of what exactly is required and then try to find the person if that is deemed necessary.
We're able to go through a legal process here that allows us to adopt even when the father is not accepting the adoption or he's not responding / unable to contact him and especially if he's not paying child support or doesn't fulfil his legal obligations.

「How would we contact the ex husband if we don't even know where he is or if he is even alive?」
「why would we need his consent if he practically abandoned them.」

Those are definitely questions for a family law layer, unless you're expecting someone on this forum to volunteer to hunt the father down or find his corpse, depending on whether or not he's still alive.

Those questions are better aimed at american lawyers. Not a Japanese tourism website.

I'm just trying to see if anybody has been in this situation before, and if so, what was the process that they had to do.

I think there is nothing wrong and difficult with this. You just need to process the legal papers for the kid to be transferred under you. Since the mother is also under you, you won't really have a difficult time. It is also highly recommended to choose an accredited and approved adoption service provider to also help you process the papers needed. It will also not take a long time, especially if there are no problems and if the process is smooth. Most of the time, it will take at least 180 days. Good luck to you and your wife.