I think the way to introduce SWORD (using my idea of them being SHIELD's response to the alien attack on New York ---> leading to SHIELD starting an alien defense agency) would be easily shown in a Captain Marvel film.
Carol Danvers is a former pilot, former SHIELD agent, who is now working in SWORD (Sentient World Observation and Response Department) an agency created by SHIELD in response to the arrival of Thor, Loki, and the alien attack on New York. Its headed by Abigale Brande. Carol, a field agent, is plunged into the middle of a Kree battle on Earth as Captain Mar-Vell fights against Yon-Rogg and his renegade Kree troop. Eventually this leads to Mar-Vell sacrificing his life and Carol getting his powers and becoming Captain Marvel.
The idea though is that the SWORD agency has already been started, just like SHIELD was in Iron Man, or the Avengers. Its already an agency, a brief explanation as to why they were created would be given in a sentence, like when Fury explained in the Avengers why SHIELD was creating Hydra weapons based on the cosmic cube. He says its because of Thor. All that would need to be said would be that SHIELD needed to create a defense for Earth, something like that.
Putting it in a movie like Captain Marvel would have the agency center stage but not the star, not overly explained or making them and their origins the focus of the film.
Abigail Brande and other SWORD agents would play as much a role as SHIELD played in the Avengers or Iron Man 2. Minor but still there. Also similar to how they were portrayed in EMH cartoon when Carol was introduced as Miss Marvel.
Just some thoughts on how I would do it.