When you should start the loan application process will depend on your scenario and a few factors. If you are purchasing a property (or lot) at the same time you closing on the construction loan, you should apply as soon as you have an agreement with the seller to buy the property.
If you already own the property, people will typically apply when the plans and budget are a few weeks away from completion. This way the lender can get the processing and approval out of the way while the plans and budget are being completed. Once those items are complete, the appraisal can be ordered. So when the appraisal comes back, your loan will already be approved subject to the appraisal. Final approval can then be received once the appraisal is signed off.