It's doubtful. The shelters are usually looking for foster parents with dog owning experience. They are VERY picky when choosing them.
Can I foster a dog if I never had a dog before (first-time dog carer)?
Contact some of the rescue groups they're always looking for foster homes, they should give you any help you need to deal with problems and can start you off with a dog that's easy to handle. They'll be delighted to hear from you I promise.
Anytime you want to as long as you have the capability to provide the needs of a particular animal you want to have. Just bare in your mind that it takes a great responsibility and effort that the moment you take it, you should learn to love it.