My wife and I helped form a 501c3 non profit a few years ago. Operating in conjunction with the nonprofit was a coffee shop (formed as a C-Corp). On January 1st of 2018 my wife and I formed an LLC and took over operation of the coffee shop. We did not "buy" the shop, but we did assume the debt as well as inventory, furniture and equipment (assets).

Would that debt minus assets be considered our startup costs?

no Some expenses you might have during the startup phase of your business are not deductible as startup costs, including Costs of buying business assets (like a building, equipment, or vehicles). These costs are considered separately for tax purposes

But they are costs that could potentially lower my tax liability?

But they are costs that could potentially lower my tax liability?