When does a new Luxembourg company file for a VAT number?

Within 15 days of starting a taxable activity, by filing an initial declaration with the Administration de l'enregistrement, des domaines et de la TVA (AED). The estimated turnover in that declaration sets how often you file VAT returns. The AED then issues the VAT identification number used on invoices.

Source: Inscription à la TVA, Guichet.lu, Government of Luxembourg