How do I control materials on site so they don't go missing?

Short answer

Receive every delivery on site and record the quantity actually unloaded, not the quantity ordered.
Photograph the delivery and attach the photo to that day in the site journal.
Allocate consumption to the stage the material was used on, not to the site in general.
Periodically compare recorded consumption against the bill of quantities, on the expensive items.
Investigate any gap larger than normal wastage while the crew is still on site.

Order 2634/2015 on financial and accounting documents — material receipts are evidenced by a delivery note or goods received note, and consumption by a material issue note.
Accounting Law 82/1991 — material stocks are managed against documents and verified by stocktaking.
Regulation (EU) No 305/2011 on construction products — materials incorporated into the works must carry a declaration of performance and CE marking, and their paperwork belongs in the construction technical logbook.
Law 10/1995 on construction quality — using products without conformity documents leaves the contractor liable, regardless of who bought the material.

Example: on a 12-apartment site the bill of quantities allows 1,290 m² of floor tiles plus 5% wastage, i.e. 1,355 m². Recorded consumption reaches 1,520 m². The 165 m² gap, at 70 RON/m², is 11,550 RON that never made it into the building.
Example: a 24 t cement order is unloaded as 22.4 t weighed at the gate. Recorded that day, with a photo of the weighbridge ticket, the shortfall is settled with the supplier that month rather than at year-end stocktaking.

Signing for the material against the ordered quantity, without checking what was actually unloaded.
Not allocating consumption to stages, so you can never say which piece of work overconsumed.
Comparing consumption with the bill of quantities only at the end, when there is nobody left to ask.
Leaving expensive materials — copper, tiles, joinery — without a daily record, on the assumption it will show up at the end anyway.

Deliveries and consumption are logged in the daily journal, straight from site, with photos attached to the day.
Material consumption feeds the project's materials cost centre automatically.
The overrun alert on the materials cost centre fires during execution, not at final account.
Consumption is visible per stage, so discrepancies surface at the stage that caused them.