I Think....
....That Tappan introduced these ovens to the consumer market in '54. I have seen references to them as early as that. However, most sources on the Internet say 1955, which could mean that Tappan introduced them in late '54 for the 1955 model year.
The basic idea behind microwave ovens was discovered at Raytheon in 1945. Raytheon wasted no time getting microwaves into the hands of the U.S. military, in 1947. There was also a demonstration to the public in Boston, using hot dogs. Microwave ovens began being used in restaurants and food-service applications. For a time, the Stouffer's chain based much of its concept on centrally-produced food shipped frozen and then microwaved in its restaurants. The restaurants are gone, but Stouffer's frozen food is still going strong in grocery stores.
The Tappan microwave didn't sell too well, due to a staggering list price of $1295 in 1954 dollars (equal to more than $11,000 now). Things kind of sat there until 1967, when Amana introduced the countertop Radarange at $495. That was still very expensive (like $3,500 today), but not out of the question for luxury households. The 1967 Radarange (the RR-1) was the "breakthrough" machine that began making people want a microwave oven.