RFC and CFDI in Mexico: how does a foreign company start invoicing?

Another question that comes up in many market entries: a foreign company or startup closes its first client in Mexico and needs an RFC (the Mexican tax ID) and valid electronic invoices (CFDI).

How did you or your clients solve it?

• Did you set up a Mexican entity from day one, or start by invoicing from abroad?
• How long did it take to get the RFC and to issue CFDI?
• In the meantime, did a trading company or a distributor invoice for you, or did you hire your first people through an employer of record in Mexico?
• Which mistake cost you the most time or money?

Answers from accountants and lawyers in the network are especially welcome, in English or Spanish.