In a large bowl, mix together all of the meat, thyme, salt, pepper, 1 cup BBQ sauce, and breadcrumbs. Add more BBQ sauce or breadcrumbs as needed.
Heat the oil in the inner pot of the Instant Pot using the sauté setting on high. Add the onions and cook until brown. As they are starting to brown in the pot, add 1/3 cup BBQ sauce to caramelize them.
When done, turn off the Instant Pot and remove the onions. Add them to the large bowl with the meat mixture.
Pour the stock into the bottom of the Instant Pot, and set the trivet that came with your Instant Pot in the bottom of the inner pot.
Make uniformly sized balls and set them onto the trivet. Layering the meatballs is perfectly fine, just try not to flatten the bottom ones by pushing down. Optional: brush a little more BBQ sauce on top of the formed meatballs.
Check your sealing ring and then twist on the locking lid. Set the valve to sealing and select Manual mode for 6 minutes.
When the pressurized cook time has ended, let the Instant Pot naturally pressure release for an additional 6 minutes before carefully manually releasing the rest of the pressure.
Strain the meatballs.
Let the meatballs cool for a few minutes before plating.