1. If the items in question genuinely are part of the cost of the items you will be selling they should be Inventory until sold when they become COGS.
2. Logo design and special design software purchased before you begin making sales should qualify as start up costs. (see resource below)
3. The date you form the entity is often not the date it "begins" operations. The IRS considers the "month the business begins to operate active trade or as a business" as when operations begin.
4. Start up costs can and are often utilized in the first year of business.
Here is a well written article published in Tax Adviser https://www.thetaxadviser.com/issues/2017/sep/deducting-startup-expansion-costs.html
