The first iteration of this design honestly isn't even an iteration.

I know the final product I'm looking for is nothing like what v0.1 turned out to be, but I needed to know that I could:

1. Solder the chip to the board
2. Design a capable board
3. Select the correct components for proper functionality

I'll give full credit to the TPS61022 datasheet, which directly gives (thank you TI) a recommended pcb layout along with an example circuit which input a ~3V signal and output 5V, conveniently close to my original use case:

They really made my life easy. I opened up Kicad, copied the schematic over, and laid my pcb exactly how the datasheet showed. They do stress a few things such as the distance of the capacitors to the TPS61022, but other than that, it seems pretty straightforward. For the inductor choice, there wasn't too much thought put into this other than this snippet from the datasheet: The TPS61022 is designed to work with inductor values between 0.33 µH and 2.9 µH.

This was actually the first pcb I'd designed from scratch, hence the absence of a ground plane and a single trace on the bottom layer. The design rules checked out, though, so I exported the production files, uploaded them to JLCPCB and a few weeks later got the bare pcbs. 

I ordered a stencil for this, because, well you need one. For stencil alignment, I 3d printed a small jig to hold both the board and stencil in place while I pushed the paste through. 

After that, the components were placed and off to the hot plate. I turned it up to 200 C and once I got that nice flow, I shut it off, let it cool, and could finally test it!

Now, I don't have an oscilloscope, so I can't zoom into the output voltage waveform, but a stable reading on the multimeter is good enough for me to start work on v0.2.

Also note that I didn't actually pass through any load, so again, I'm not aware of the limitations or even the performance of this setup once it's actually in use.