Correct; additionally, if you're in a unique unit, there is probably a good chance you have items that don't have TMs. Use the fielding documents for those items items (ie make a copy of the documents and inventory off of those). I still have my original inventory documents (I did not have a supply sergeant either).
The only possible way you can go wrong from here is if the equipment is entered in wrong into GCSSA. I was a wizard with PBUSE but know nothing about GCSSA. If it's similar, you will run into issues with 1. COEI/BII listings not matching in the database, 2. manual input errors when transferring initial inventory results in the computer, and 3. "resets" of database material.
To address 1., use your best judgement when matching the database to the TM; look at NSNs, item descriptions, etc. Write down on the inventory copies what was wrong and how you addressed it. For me, I had components of certain kits that were doubled in PBUSE. Even though the kit was complete via the inventory, I had to zero equipment out in PBUSE because it didn't match the TM.
For 2., put in the hours. I probably had about 50 hours of reconciling input errors or inconsistencies (usually arising from problems related to 1.).
For 3., nothing you can control. With PBUSE, the updates at the end would wipe clean the tracked shortages when some items were updated. You will have two paper copies to verify this against when this happens (the signed document and your original inventory copies).
In all honesty, the only way people get charged for property is if they seem negligent or lazy. If you are well organized and communicate problems to your supervisor, you will be fine. There were definitely moments when either the "new hotness" equipment I had were missing items when it reality it was a failure to communicate to the COC. Or times when the 50+ old items don't even have legitimate TMs anymore but their components are listed in PBUSE. Know your equipment and you will be fine; I had the luck of being a PL and an XO before I signed for equipment but it is not hard if you apply common sense. And do not trust everything you hear; people you think would know about property often don't (supply sergeants, battalion xos, logistics officers, etc).
This is only the start of what you will learn with property; you will naturally learn about receiving new end items (ie lateral transfers or fieldings), receiving ordered supplies and accounting for those (new screwdriver comes in, make sure the property holder signs for it), and you probably already know about cyclic/sensitive inventories.