There is no minimum. It's whatever the court order says. In theory it could be zero, though this is very rare. You should propose whatever you feel is best for your child. If he has a history of domestic violence, emotional illness, addiction, alcoholism, child abuse, or abandonment you may get restrictions on his contact with the child under RCW 26.09.191. Good luck.
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I think you are wise to do so for a number of reasons. Fathers who have no rights can sometimes use that as an excuse to walk away. Over time a reluctant father can come to the tabel of parenthood if he can get beyond his feelings of resentment and such. Over time sheer curiosity can erode the harshest of denials.
Moving to your specific question, there is no minimum time but courts commonly order alternate weekends one the child is old enough. Infants should not be away from their mother for overnights unless they are previously well bonded with their father. So if you child is very young it is wise to put in four hour blocks of time 2x a week. At age 2 it could be most of a weekend day. Overnights could begin at age 5.
Since you have no idea what he wishes I suggest you put in an schedule that grows as your child grows as noted above. Holidays should be alternated and summer vacations can escalate a week a year up to 4-5 weeks if you wish.
Remember also that if the father does not exercise his time for a long time you can seek more support. Some courts have found fathers in contempt of court for non-exercise of time. This causes some dads to see the light and others to passive aggressively retaliate with the child..
In sum there are many many factors to consider in drafting a parenting plan that protects you and your child while promoting contact. You should talk with counsel about this as the personalities and the history need to be considered before making the final plan.
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