Filing GreenCard through sponsorship (EB2or EB3) is a lengthy process and you need to understand all the steps before applying for it. Do some online study on how it can be applied through sponsor company.
In brief, it has three major steps.
step1: Labor certification (PERM)
step2: I-140 Approval
Step3: 765 (EAD, i.e. work authorization), I-131 (Advance Parole) and I-485 (Green Card)
If step 1 is approved, you can file for step2 and step3 concurrently. All these processes has its own processing time.
Now, if you company (consultancy) agreed to file a GC for you, they can do so only if you are already working for them for some client project, unless its a direct hire.
I see you have undergrad, then you are eligible for EB3 category with some years of experience. Since your degree is mgmt, and worked in BA, you can still file. Talk to your consultancy if they are ready to file GC from day 1 when you join them. Hope it helps. If you need to know more, message me.