I have a flight in a month with AC back to the USA from Canada. I needed to add an infant to the ticket and I have been unable to do it.

Whenever I call the call center, they are at a 2hr+ wait. I've tried waiting 3 hours and still didn't get an agent.

I've tried doing it online but I don't see the option.

What are my options? This is pretty ridiculous.

You call them, put your phone on speaker, and then go do something else for a while.

Note that with AC (unlike some US airlines) you can actually add the infant at the time of booking/purchase.

Unfortunately AMEX did not allow adding the infant. It would error out.

Do I have to add the infant in advance for the international CA to USA flight or can I do it during luggage drop off and checkin on the day of flying? Any potential problems there?

Is this not something you need to do through your TA?

Or use "hold for me" on an Android phone

You can do this, but there are some caveats:
a) Some aircraft have one side that has the extra oxygen mask and the other side that doesn't. If you wait until DoD to add the infant, it may require moving of seats and separating your family if there aren't seats together on the correct side of the aircraft
b) Have to use full service line at the airport which can be unpredictable
c) Sometimes they block the middle seat for you if you have an infant
d) Not relevant here, but if it were a longhaul, having the infant will give you priority for the bulkhead/bassinet
e) not sure about this one, but aircraft may have total pax capacity restrictions that mean they can only take X number of lap children on a completely full flight due to exit/raft/life jacket capacity

A transborder lap infant requires a real ticket to pay for the per-head border crossing line items. You can do it at the airport but I�d fully expect many agents to just call ticketing� with egregious hold times as everywhere else in the system. Plan accordingly.