Your tax home can be your place of residence without claiming office in the home there.
You start there with some orders for the first delivery.
You cannot deduct the commute to the day job, unless you are going there directly from a delivery and not your tax home.
The same is true on the way home from the day job - no commute is deductible, unless you are going directly to a delivery.
Keep a detailed log of your miles and trips for tax purposes.
This link may be helpful: https://turbotax.intuit.com/tax-tips/small-business-taxes/business-use-of-vehicles/L6hi0zzzh
