I have no references. If I am able to book a date with an agency, will they later serve as a reference? How does that work? Do I ask them if it's OK first

I would inquire about it first just to make sure that is the way go want to start your hobby life, another alternative that will make your case a bit better are the verification sites such as P411 and Date-check, there you can gain Oks that you can use as a reference in some cases,  some ladies there are newbie friendly FYI  but be aware that regardless of which way you want to go, agencies and verification services will require your work info and agencies are more likely to get in some sort of trouble sooner or later, less so an independent lady.

not all indies will accept references from an agency.

For many, it is still a very good way to start. Also some agencies are more friendly with the provider community in their area than others. Some are constantly at odds with the indy community, some are quite friendly. A post on your local board might help in this area.

I'm thinking of a well known agency in Boston that does not provide references and will not even provide an "OK" or confirm a "We Met" on Date-Check (even though they advertise there). That's just their policy, even if you've used their services around 10 times.