How is a new airport certified or approved to operate by international organizations?

Question

I just read the news of a new airport in construction in Mexico (Mexico City). They seem to be starting operations in a few months.

In this case, researching a bit, it seems domestic and a Venezuelan airline already had flights to and from that location, and I think only Aeromexico refused to change the hub.

I don't know if the airlines are fined or issued an admonition for landing in a aerodrome/airport, AFAIK without certification. IMHO, this is risky thing to do. It reminds me of HKG being transferred from Kai Tak to Chek Lap Kok, but it was a smart idea since the former HKG was amidst a tall buildings zone. In the case of Mexico's new terminal, there does not seem to be a practical reason to make a new one in the area.

So it makes me wonder: How is a new airport certified by ICAO/IATA/EASA/FAA?

Researching a bit more, this new airport was done scrapping a former project to build terminals 3 and 4 on the actual MMMX (I don't understand Spanish that well, but there is allegiance to turmoil rubbish to do so). The navigability studies were made by NAVBLUE.
And this is an already in operations air force base with a number of operations of that is been retrofitted to admit commercial planes, Thus it makes me more curious to my question.

Answer 1

The airport is regulated in general use by the local authority. The local country will designate some airports for regular customs and immigration services. There is a tiny airport near me that is designated as an "international airport" and has regular customs personnel but the runway is too small for any airline. (3000ft/900m long and 60ft/20m wide, surrounded by trees too).

Airlines individually approve each airport that they intend to use regardless of other airport regulations. Each airline has its own set of researched and approved runways, approaches, pilot training, weather conditions, times of day or night, and aircraft combinations. They do many calculations before they ever schedule a flight to know if the airport is suitable for their specific operation.

Airlines file paperwork with border control before the flight which includes the intended airport of landing. Also by the treaties of the Chicago Convention international aircraft are allowed to land at and take off from any public airport for purposes of fuel and maintenance. However, this does not give permission to load or unload pax/cargo or for the crew to leave the airport by ground.