It's not exactly some unsolvable logic puzzle. This is a problem not everywhere has, it's pretty simple.

Two solutions.

First, you create a second way in. It can be anything from dedicated streets for cargo with all the loading docks to shared warehouses at the edge of the city and underground tunnels like Disney. The main idea is to dedicate most streets to people and bikes, which can have all the storefronts

Or the easy way we could do far more quickly... Instead of slicing space you slice time. Limit deliveries from 4am to 7am, maybe an afternoon slot if necessary. The idea being people get the prime time, and you work out the logistics with that constraint

For better logistics, limit the size of the trucks and do shared distribution centers as a buffer for normal shipping times.

Ideally, you do #2 while transitioning to #1. Put a slowly increasing off hour delivery tax and create an incentive. The logistics will magically come together as the tax grows