Yes, you can claim your business startup expenses, but not on your 2016 tax return. The general rule is that business startup expenses are deductible in the year when active trade or business begins. Since you had no income-generating events in 2016, your startup expenses will become deductible in 2017, when your new business begins to generate revenue. Please see IRS Pub. 535 Business Expenses for more information.
Also, you must distinguish between startup expenses and the amount spent on business assets (machines, equipment, vehicles, etc.). These assets are depreciable over their useful life, although in many cases can be expensed in the first year put in service under Section 179 of the Internal Revenue Code. When you are ready to file your 2017 tax return, TurboTax Self-Employed (if it is a disregarded single-member LLC) or TurboTaxBusiness (if you have a multi-member LLC) will guide you through the steps to enter information about these assets and make the correct choices to expense or depreciate their value.