Add oil to pot and add thighs skin-side down. Cook, in batches if needed, until golden and crisp, 3 to 5 minutes, then flip and cook 3 minutes more. Remove chicken from pot.
Add garlic to pot and cook until fragrant, 1 minute. Add water or chicken broth and thyme sprigs, and use a wooden spoon to scrape the brown bits off the bottom of the pot.
Fit Instant Pot with trivet and place thighs skin side up. Secure lid and press the manual setting. Cook on high for 12 minutes and then naturally release pressure.