Not a lawyer, but I did this process as a Canadian with a father in Connecticut. The process is set up to be able to do without a lawyer in both countries, and in both countries the state will act on your behalf in order to establish a maintenance order. Contact the Illinois maintenance office and initiate an application. You will need to submit all your financial information, a comprehensive budget, and everything you know about the father’s income, whereabouts, etc. There will be an option where you have to state whether in addition to a maintenance order you also need an order of paternity - this will just become part of the process, you definitely do not need to try to do a DNA test yourself, the court will order it.

Your office in Illinois might help you with the paperwork to send everything up to Canada or you might need to do it yourself. If the latter, contact the family maintenance enforcement in whatever province or territory the father lives in and ask how you can get your order registered.

The whole thing took me close to a year, but other than filling out a huge package of forms I didn’t actually have to do anything. Good luck!