You mentioned in your question that the bill would have been paid by the insurance plan. In the US, insurance plans have timely filing deadlines - they vary from plan to plan, but can be as short as 90 days. Providers under contract with the plan are not allowed to bill the plan or the patient after that deadline, the debt is essentially a write off at that point. So, while you wait for the debt collector to validate the collection, the place to start is with your insurance plan - make sure the provider is in network and the services are covered. If they are, and the plan never received the claim, ask the plan to help communicate with the provider. Usually a provider will give up on a small bill like this under pressure from an insurance plan they're under contract with.
If the plan did receive the claim prior to the deadline, but didn't pay it for some reason, you will need to work with them to understand what happened - mainly, why you didn't receive an EOB explaining their decision (which they're required to provide) - and you can ask them to handle the provider for you.
If the provider isn't in network or otherwise has no affiliation with the plan, your next step is to contact the hospital and ask them why this provider's bill is being submitted separately from the rest of their services. Some types of providers are stereotypically bad about billing within hospital guidelines (i.e. anesthesiologists will sometimes automatically submit their own bills even though their services may be covered by the hospital's billing). Sometimes these situations occur because an in-network hospital will bring in one out of network provider to do one specific service for something as complicated as a pregnancy. If the hospital did this, they're responsible for negotiating payment with the provider and your insurance plan, the provider can't directly bill you (even though many will, out of automated-billing-induced ignorance). In these cases, the hospital will usually be willing to help deal with the provider to get the bill handled correctly.
As a last resort, you can contact the provider directly and ask for an explanation. Maybe they had your address wrong or were otherwise operating under the assumption that you were receiving bill(s) and notices about the money due. Or maybe there was an issue in their system that stopped them from billing you. Even if the insurance won't cover the services and has no leverage because the provider is out of network, or the provider is claiming they did bill correctly (and you somehow never got the bill), providers generally aren't in the business of beating people up over money and are usually happy to negotiate some sort of settlement.
All of the above steps should (hopefully) resolve the debt in a way that makes the collection attempt illegitimate. The plan, hospital, or provider should resolve that with the collections agency. If the debt is resolved through no fault of your own, and the collection account doesn't disappear off your credit report, you can contact the credit bureaus directly and file a dispute, providing them with whatever documentation you get as a result of the settlement, and the bureaus will remove the account from your report. If it turns out it was your fault (you received a bill but didn't remember, or something) you can still negotiate a "pay to remove" settlement with the collector. There's lots of good info on google about dealing with collections that are valid, so that may be a good step if it's a valid collection.