Call the transpoerter's office, provide them the LR no and details of Goods movement and ask them, following:-
1. Are you registered under GST? (in case LR or any doc that they issued does not show their GSTIN).
If they say they are UNREGISTERED, then book RCM liability under CGST & SGST.
If they are REGISTERED, then ask them to check and revert at the earliest with their GSTIN they will use to report your transaction under GSTR-1.
I know it is a tiresome exercise, but (with registered GTA's) once you get an idea how they determine which GSTIN to use, you can make a note for future reference.
Based on my experience so far, a registered GTA will mention a GSTIN on the LR that it is going to use to report your transaction in their GSTR-1.
Very rarely do they Not mention a GSTIN, or will report the transaction under another GST No. That is why you call them the first time.
You should, also cross-check your GSTR-2A for that month. If they have already reported the transaction, then make adjustments to your entry accordingly (if required) and report in your GSTR-3B.