You already run a warehouse
If stock sits on a shelf between receiving and shipping, even for a day, you're running a warehouse. The only question is whether you know where each item is.
Why bins matter
A bin is a specific shelf or slot. When every item has a bin, picking stops being a search, counts stop being a guess, and a partial receipt doesn't vanish into a corner.
Start with receiving
Put stock away to a bin at the moment you receive it against the PO. That one habit gives you accurate quantities without a separate data-entry step.
Pick from the order, not from memory
When an order is ready to ship, the pick list should say which bin to go to. Someone new can fulfil an order on their first day.
Keep it small
You don't need racking software or barcodes on day one. A handful of named bins and the habit of using them is enough to start.