Here's how this would go down in BC:
1. Start an action in Provincial Court (probably Queen's Bench elsewhere) seeking joint guardianship and specified access (i.e. you get to see her on X days for Y number of hours) as opposed to "reasonable and generous access" which leaves too much power for the custodial parent to play games. You'll have to do this in the registry closest to where the child is living. You could try elsewhere, but that's where it will end up.
2. You'll likely be hit with a counterclaim for child support. There won't be a lot of argument about the number as there are Child Support Guidelines that tie support amounts to income. If you've made good faith efforts to pay some amounts in the past and are not subject to a previous support order that you've breached, there's a chance any support order will be forward looking (i.e. no arrears).
3. If the mom intends to oppose your application, you'll have a first appearance in front of a judge. Again stressing that my knowledge applies only to BC, this first appearance would likely just be to set a date for a Family Case Conference (assuming there are no pressing matters that need immediate action such as the child being in physical danger) so if you've hired a lawyer, the lawyer can handle it on his/her own.
4. You'll have a FCC, which is like a mediation session in front of a judge, where you'll state your case for why you should have access. If terms can be agreed upon by both sides, you can get an order, if not, you'll have to set a date for trial.
As was alluded to above, the a priori position of the court is to maximize the child's contact with both parents, so unless you're a deadbeat, you'll get some access likely including regular telephone and/or email access. What that access ends up being specifically depends on a lot of things, including the child's age, current comfort level with you, the logistics of making travel work, etc. It could up anywhere from you only getting to visit in the child's home with a supervisor present to you having the right to have the child visit for designated periods with both parties sharing transport costs.
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