First.. Get a trust. If you're going through silencer shop, you can purchase one of their boiler plate trusts. If you don't like that, there are plenty of other online NFA gun trusts. Not endorsing - I got mine through
NFA Gun Trust - Now Only $79 [now for $79].
Get a trust even if you're the only one that would be using it. It saves a bit of hassle if you change your mind down the road (eg, you get married/your SO enjoys firearms, your family members/friends want to borrow said items legally while you are out of town). Having it done as an individual means you, and only you, can posses said items. Unless you sell them. Make your TRUST NAME SHORT. Mine is <Last Name> Trust. Don't do <First name> <Last Name> National Firearms Act Revocable Living Trust. Because you have to engrave the ENTIRE Trust name on your firearm....
Second... Have your lower receiver engraved as required by the NFA. Do this before submitting paperwork in case the engraver messes up!
Third... Submit the paperwork for BOTH ASAP. The longer you wait to submit the paperwork, the longer you will wait for your tax stamp. Period. SilencerShop will submit all of the paperwork for a Form 4 (suppressor). You aren't purchasing an SBR from them, so I doubt that they will submit the Form 1 paperwork on your behalf.
Fourth.. Wait. You acquire the suppressor when the Form 4 is approved and returned to your FFL. If you don't live in Texas, and you purchase from SilencerShop, you will also need to wait for a Form 3 to be processed which transfers the item from SilencerShop in Texas to your local FFL SOT.
Fifth.. When you receive your Form 1 SBR paperwork back approved, THEN you can send your barrel out for cutting and threading. Note - the length you specify on the Form 1 does NOT need to match the actual barrel length; there is no requirement that this be done in the law, and nothing prohibits you from 'changing your mind'.
I have multiple SBRs and suppressors; this is the process.....
HTH