In order to resume contact with your child you are obviously going to have to locate an address - either where the child lives, or where you know the mother has regular contact with the occupant, so that you can use that address for service of your application for a child arrangements order.
You can also inform the court on your application form that you have no idea where the child is, except for a general location, and it is possible that the court can track the mother down via the DWP, or other sources.
To apply for a child arrangements order you would normally have to attend a MIAM - so you will need to speak to a mediator and get your form signed off by them. Obviously they will not be able to contact the mother, so this is more an exercise in meeting the legal requirements to make your application.
Then you need to complete the form C100 and send it off to your local family court - it would normally be the family court local to where the child lives, but as you do not know that information it will have to be your local court. The court will list the matter for a hearing - contact the mother by their methods if needs be - and then CAFCASS, social workers, will contact both parties to find out what happened, undertake background checks and then file a safeguarding letter to court recommending what the court should do next.
You will both be invited to the first hearing and the court will take the matter forward from there.