Gundam started the real giant robot craze in 1978, even though there had been series around in Japan a long time before then.
Superdimension (Space)Fortress Macross debuted in 1982, the same year that Takara released a toy series called Diaclone (or Diacrone, for an inflexible reading of the kana).
Incidental aside. Around this same time, the Superdimension "trilogy" of three unrelated series also included Superdimension Cavalry Southern Cross and Superdimension Century Orguss. And around the same time, again, there was a show and toy line called Genesis Climber M.O.S.P.E.A.D.A.
The common thread through all of these and more (like Gundam 0083) was giant robots controlled by human pilots. No AI.
Hasbro and Marvel collaborated to import most of Takara's Diaclone line and some of the toys from other lines (like Microman) as sentient alien robots called Transformers. The comic debuted in the late Spring of 1984, and the cartoon followed next September.
Carl Macek wanted to import Macross, but it didn't have enough episodes for American syndication. So he looked at the other contemporary offerings in Japan and selected Superdimension Cavalry Southern Cross and Genesis Climber MOSPEADA to padd the episode count. Then he wrote a completely new storyline to tie together all three series into one epic multigenerational story arc. The show was called Robotech, due to contractual obligations with the Revell model company that wanted the show as publicity for its Robotech Defenders line of model kits (imported anime kits from several different series). It debuted in 1985.
And yes, FASA lifted a BUNCH of dairobo ("giant robot") designs without permission. The list -- near as I can recall -- runs as follows:
MACROSS-- •"Stinger" (VF-1A) •"Wasp" (VF-1S) •"Phoenix Hawk" (Super VF-1S) •"Crusader" (Armored VF-1S) •"Ostscout", "Ostroc", and "Ostsol" (modified Battle Pods) •"Marauder" (Officer's Battle Pod) •"Warhammer" (Excalibur Destroid in the American version, Tomahawk in the Japanese) •"Archer" (Gladiator Destroid in the American version, Spartan in the Japanese) •"Rifleman" (Raidar-X Destroid in the American version, Defender in the Japanese) •"Longbow" (Phalanx Destroid) •And the three LAMs were the transformable versions of the VF-1A, VF-1S, and Super VF-1S...