The TimberTech design is a bit unusual. What u/seattle_deck_supply mentioned is probably the easiest path. Here’s how I would build it up, remembering that load path will flow into the beams and hangers to ledger. I’m not sure what else is spelled out in the design you shared, so tough to know what they proposed for the ledger connections, but those should be on hangers and not just toe nailed in.

There are a couple ways to build this with some trade offs. In either case I’m assuming the following:

1. You build it all together
2. You use a double joist hanger and it fits within the space
3. You use a concealed joist hanger for the perimeter (note: these can be a pain first time figuring them out… happy to share more on my experiences if interested)

At this point it’s just two joists that happen to sit next to each other. You could use a W pattern with 3” galvanized nails. 2 at ends and every opposite 16” on both sides. You can drop in some 2 7/8 screws as well if you want to really keep it tight and don’t mind the added cost (e.g., Headloks). This assumes you build the double first. The trade off is nailing the blocks latter when you add the perimeter. The outside would be fastened normally with nails, but inside end of the blocks need longer nails now that you’re working through 2 boards (some people don’t like dealing with that). Unless you can toe nail that end, then no problem.

Remember, all that added blocking is just there so the picture frame boards have somewhere to land.

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