If no funding is available at the time of admission, what are the chances of getting funding later, and when would I find out?
Yes it is possible, but more likely during the PhD level (it happened to three friends of mine). So basically they got the acceptance letter, they might even gave an initial fee (e.g., for first 3 months); and then, the supervisor worked out how to apply for a funding from the university or put them in a funded project.