You start deducting expenses (including Start Up Expenses) when the business is 'open'.  If it is "not operational" until January, that is when you would first start to use deductions.

In the event the business is a Corporation, you still need to file a tax return, even if the business is not yet 'open' and don't have any income or deductible expenses.

Generally, you can only deduct business expenses from business income.  You deal with your startup costs in the first year your business is "open" and has income.

Startup costs up to $5,000 can be deducted (with certain limits).  Startup costs over $5000 must be amortized over 15 years; startup costs under $5000 can also be amortized if you want to.  See here for more  https://www.irs.gov/uac/about-publication-535

I have the same question as the original poster. S/He asked should she put off start up cost purchases until January when the business will get going? OR can she make the purchases in December and deduct them starting in January? (Basically is it smarter for her to wait until January to make purchases of these start up costs?

The answer is still the same. If you have start up costs in 2020, but your business is not active until 2021, then you will deduct your start up costs in 2021. Depending on the amount of the costs, they might be Deductible as an expense in 2021, or you might have to amortize them over 15 years.  You have a bit more flexibility with treating your start up costs if they occur in the same year that your business is first active. But ultimately, it depends on much more then income taxes.   If you hold off on your start up expenses, will that delay the start of earning income? Will your start up costs be $5 for business cards or $100,000 to lease a store and buy equipment and furniture?  We can’t really advise you on your specific situation.