Doesn't make a difference. The court would still have to recognize paternity. Dad would stand equal to you in relation to custody ... expect a long distance visitation plan put in place where your child travels to Hawaii for long breaks and summers.
While dad is obviously going to stand equal in relation to custody the best interest of the child also factors in, and since mom said:
Also, I'm wondering about how to get visitations with the father in papers as well.
its pretty clear that mom is prepared for dad to have parenting time.
While I understand why you emphasize the whole "both parents stand equal in initial custody determinations" I seriously doubt that you intend to scare off unwed parents from even filing to get custody/parenting time orders established. If I were an unwed parent in Ohio and some random attorney told me that I could lose primary custody of my child by simply trying to get things legally ordered...in a situation where clearly the best interest of the child would be to remain with one parent or the other, I would tend to say heck no, I am not starting anything.
I seriously understand why you want both parents to understand that they are equal. However lets be real. Military parent who is stationed in Hawaii vs non military parent who lives in Ohio with the child...equal standing or not, we all know who is going to get primary custody...particularly if the child is an infant or toddler.
And particularly since I KNOW that you are all about the best interest of the child, and you would NEVER advocate sending an infant or toddler to live with a parent they don't even really know unless the known parent is completely unfit.