Well from my experience, if the workers like you then they will find ways to make it happen. If they don't like you then they will throw up all kinds of roadblocks. Where I live, there are even programs to get free cribs and carseats for some foster parents. So, just be wary. If they're putting up lots of roadblocks then they might be subtly trying to get rid of you. Just be careful.
I say that because if you have workers who do not like you, then your foster parenting experience will be hell. So if you're getting that vibe from them it might be a good idea to check out other options (another worker, another agency, another path to parenthood, etc).
There are laws, sure. But in my experience, the workers only obey the law when they want to. They actually legally have a lot of leeway and can ignore any of the licensing regulations if they want to. There's some clause that basically says they have full authority to determine if a home is a "suitable foster home" and can license a home that doesn't meet basic requirements. They issue waivers and special licenses all the time for their friends.
We never needed the bed or carseat until the actual child was in our home. So we could always just go get it the day of the phone call. There' a big cost to that, but we always knew that in a month or so we'd get a reimbursement check from the state that would probably cover the costs.
I'm not trying to scare you or put a damper on things, it's just that you should go into this with your eyes open. You may very well need to buy the crib and carseat now for your licensing but keep in mind that if they continue to change the rules then it's probably not about the rules; it's probably something else going on.
All that said, you can get a crib off craigslist for cheap. Buy a new mattress though. Those are only about $50. Start small if you have to and just get one bed instead of a crib and a bunk bed. Personally, I always buy carseats brand-new because people sell used ones and they lie about recalls or car accidents, etc. Luckily, you can find inexpensive carseats at places like BigLots and Tuesday Morning. Or you can borrow them from a friend just for the inspection. There's no rule about proving ownership as far as I know. You should just install it in your car and that's that.
Honestly, it's very sad, but I have yet to meet any foster parents in my area who know how to properly install carseats or use the right ones for the ages. It's incredibly depressing actually as there is absolutely no one truly monitoring carseat use! My last licensing renewal they just wanted photos of the carseats emailed to them. No proof of ownership, no proof of knowledge on how to install, and no one actually came out to look at our cars. Pathetic. I could have just gone down to target, taking a picture and emailed it without having bought the carseat at all.
Sorry, I'm a little angry right now as I'm sure you can tell. After 3 years as a foster parent I closed my home. And this is why. The system is a joke. The workers are so lazy/overworked that a role of the dice is more certain than the law.