Additional logic is required in the motherboard's chipset which your Toshiba does not have (after a review of its specifications, linked in your question above). So, it will not work.
Also, PCIe SSDs AKA NVMe have a slightly different connector than SATA SSDs as shown below.
I can't see an M.2 connector in the photo, so I looked for other photos, and found a wider and sharper photo from this page. There's no connector for any M.2 drive, so you must use a 2.5" SATA SSD to replace the original Toshiba MQ02ABD100H HDD. Here's a video showing how to open it up.
What you had circled to the right above the ribbon cable connecting the motherboard to an i/o daughterboard is where an M.2 connector might have gone, as evidenced by the post which looks like the right size to hold a fastening screw for the left side of an M.2 card, but there's no connector for it at the left side on the circuit board. It's very common to reuse circuit boards for different models and only put the connectors on the board which are required for a specific model.