The first hurdle is called the CLEO sign off. You take you completed paperwork to a Chief Law Enforcement Officer and he signs that he knows of no lawful reason Suppressors can't be owned in your area. Most use a Sheriff but not all Sheriffs will sign. Some use Police Chiefs and some use Attourneys General but it is archaic because the CLEO could arbitrarily decide he does not sign NFA forms or only some types of NFA forms. If they are Anti 2A then they can deny a lawful applicant a lawful item for a lawful purpose with no recourse other than to try and find another CLEO or go the NFA Trust route which needs a whole seperate thread. Back in the 1920's the Feds didn't know if a person could legally own a machine gun. So they asked for the CLEO to sign that the person was t a criminal and MGs were lawful in that jurisdiction. Now the Fed does the background check and knowing if they are legal is just a click of the mouse. However they still hold the CLEO sign off for some unknown reason. Imagine having to go to a CLEO and ask for permission to buy any gun and have him say "Nope, not in my county!" Just because he can.
Once you have a CLEO sign off you get pictures and finger prints and send the package along with $200 money order to NFA branch. A couple years ago things were 12 months out. When I did my SBR last year it was down to 4 months. Time depend on amount of applicants and number of processors. When you get the approved and stamped paperwork back you can either proceed with the build or purchase of the suppressor, SBR, or MG. The only difference may be that if you go through a dealer you purchase the suppressor first but the LGS keeps posessionof it till the approved paperwork is returned. Once that happens it is yours to take home.
I should note that this is how it works in Florida but the federal end should be the same for all states. However if like
said as in NJ they are illegal then it's different as far as what products are legal in the particular state. Suppressors are not 50 state legal right now.