Extension of Visa waived entry?

Quite a unique situation I'm in:
I married a Japanese woman last year, and now we're expecting a baby boy in May. We are traveling back to Japan soon, but because the max allotted stay for Visa free entry is three months, I was planning on requesting an extension given the circumstance. That all being said, I don't have a return ticket back to the US after baby is born. Can anyone give me some advice? Should I hide this information from Japanese immigration officials? What would be a good excuse for not having a return ticket yet? Thanks ahead

Congratulations on your wedding (and the baby to come).

Whether extension of "Temporary Visitor" status under visa waiver program is allowed depends on your nationality (I believe it is granted for UK nationals up to 6 months in total, while not for US, etc.)

Any chance you are considering applying for a change of status from "Temporary Visitor" to "Spouse of Japanese National" while you are in Japan? If you plan to live in Japan, that sounds like the more suitable option.

"Given the circumstance", what circumstance? Since you say you will be travelling yo Japan, I gather that you live in another country? What exactly is your reason for wanting to stay in Japan for more than three months under temporary visitor status? I don't think "I have a young child" will be sufficient.

If you don't have a return ticket out of Japan, you may face problems at the check-in counter for your inbound-to-Japan flight up to and including not being able to board the aircraft.

If you don't have a return ticket out of Japan, you may face problems at the check-in counter for your inbound-to-Japan flight up to and including not being able to board the aircraft.

Yes, this. Even on my last flight back to Japan I had to prove to the airline before boarding that I was allowed to stay in Japan because I didn't have (or need) an onward ticket. Showing my residence card was the simple solution in my case.