Someone in your area might know more details, but in general, no.
The purpose of the homestudy is to show that you are safe people and that your home is safe for a child. It includes a background check and federal fingerprint check - both of which can take a month or more to come back all by themselves. Plus the availability of a worker to come interview you to make sure there is nothing of concern in your backgrounds - history of fighting, drinking, etc. And your references from friends/employers/family have to come back too, so the workers know nobody else has concerns about you, either. All of that is understandably required before the state will entrust a child to your care.
Same thing with the MAPP classes. They will give you valuable information about things that are reqired of foster and adoptive parents when adopting a child who is in state custody. EVERYTHING is mandated and usually different from how you would normally parent. How to discipline, when to have meals, how many feet must be between beds, what forms you have to fill out each month, when the child needs to see a doctor, the process of TPR and adoption, which children qualify for subsidy and how to apply for that, etc. All that is covered in MAPP classes.
There is just no way for you to get all the reqired clearances and information in less time. Nor can they bump you to the head of the line in front of people who signed up months ago. Nor can they ask the little girl to wait for a permenant family to see if you will pass the checks and still be interested when you learn all the stuff that is involved.
But it never hurts to ask, right? See what your own foster care adoption worker says about the chances of getting everything done quickly. See if there is a state minimum of stuff you have to get done, and maybe the 2-4 month estimate includes things that could be done afterward. But the worker who told you not to get your hopes up is right - do what you can, but don't let it devastate you if it doesn't work. Most people who wish to adopt children in foster care find many children who they could effectively parent before they find "the one" who gets matched to them.