Yes, the Americans had very good intelligence on the Mitsubishi A6M Zero-sen by the time the United States officially joined the war in December 1941. However, that intelligence was not always properly disseminated or acted upon in the earliest days of the war.
Some of the best information came from a US Navy attache in Tokyo, an aviator named Lieutenant Stephen Jurika. He attended an airshow in January 1941 where a Zero was on static display and was, incredibly, permitted to climb in the cockpit. Jurika spoke fluent Japanese and was a trained flier, who was in Japan as an official US Navy representative, yet was allowed to see the Zero. The display of the Zero included some basic information like the horsepower of the engine and the aircraft weight.^1 Noting the weight would have been significant; the lithe Zero owed much of its capability to the fact that it was far lighter than any comparable carrier fighter of World War II. The instruments inside the cockpit also likely would have revealed some basic information about its performance characteristics that he could infer with his knowledge. Jurika noted this and delivered the information to the Office of Naval Intelligence in Washington. Jurika's report made it to the Navy's Bureau of Aeronautics, which seemed to disbelieve that an aircraft with the Zero's stated performance characteristics was possible, or at least wasn't possible to be produced by the Japanese. Jurika returned to the United States in mid-1941, but no one followed up on him about his report on the Zero.
Another source of information would have been the Flying Tigers in China. Claire Lee Chenault's unit faced Zeroes in combat in China in 1941 while flying a version of the P-40, and he sent information back to military intelligence also.^2 I'm somewhat skeptical of reports of American pilots with extensive experience against Zeroes in China in 1941. By the time the American Volunteer Group was flying in 1941, the Japanese Naval Air Forces attached to the aircraft carriers of the Kido Butai were training for the attack on Pearl Harbor and not supporting the war in China. Other Japanese naval air forces did fly Zeroes, but the Japanese Army Air Forces did not fly the Zero. Much like Americans fighting German tanks often misidentified their foes as Tigers, it's likely that American pilots in China (and elsewhere) often misidentified other types of fighters for Zeroes. However, Chennault had been in China for years, and there were Zeroes that supported the Japanese war in China as early as 1940.^3 It's likely that Chennault did have some good information on the Zero, either from American or Chinese pilots, and was able to share that with military intelligence.^4
Despite two good sources of information about the new Japanese aircraft, American aviators and intelligence officers appear to have failed to grasp the ascendency of the A6M. You can chalk this up to any number of reasons; military intelligence, particularly the Office of Naval Intelligence, did not cover itself in glory in late 1941 and early 1942. The Japanese had not been at the cutting edge of aviation for much of the 1920s, consulting experts from Great Britain, France, and America to help jump-start their native aerospace manufacturing companies. Mitsubishi (which made the Zero), Nakashima, and Kawasaki led the way, but there were plenty of other companies that also joined the effort.^5 By the late 1930s the Japanese were more than capable and producing aircraft on par (or better than) what was coming out of those countries, but experts were still skeptical that Japan could produce that caliber of aircraft on its own. As early as 1938, the US Department of State imposed a "moral embargo" to strongly discourage American companies from exporting further aircraft, aircraft components, or certain tools to Japan as a result of its action in China. The embargo was formally codified with the 1940 Export Control Act. By then, however, the chicken had already flown the coop. Japan's indigenous aircraft industry was up and running.
The Americans' failure to take note of the Zero was a mistake that wouldn't last long, however. Chennault's men learned to use their aircraft's superior characteristics in a dive to gain an advantage against Zeroes.^6 Chennault also devised an early warning system that made sure his pilots were ready for Zeroes and would have enough time to gain altitude and be in good firing position.^7 USN Lieutenant Commander John Thach, an F4F pilot, reportedly read about the characteristics of the Zero in September 1941 and began thinking of ways to beat the faster, more agile plane. His solution came to be known as the "Thach Weave," or if you prefer the technical name, the "Beam Defensive Maneuver." It was designed to have one aircraft, or a group of aircraft, cross over the path of another group to give them a firing position on a Zero that was on the tail of a target. Thach practiced the maneuver by having his wingman, Edward "Butch" O'Hare (you may have flown through the airport named for him in Chicago) flying his F4F at full power, while Thach made sure he didn't use the full throttle of his own F4F to simulate the Zero's speed advantage. This was successfully used at the Battle of Midway when Thach's squadron shot down at least two, and possibly four Zeroes while executing the maneuver.^8 The information on the weave was quickly distributed to other American pilots, who were able to practice it themselves. Japanese pilots later in the war eventually developed counters to the Thach Weave, but it was an effective tactic that greatly leveled the playing field.
Some information on the Zero was also available after the attack on Pearl Harbor, where a number of Japanese Zeroes were shot down. Recovering Japanese aircraft that were shot down in the attack was a consideration and helped reveal at least some information about the capability of their aircraft. One of the more famous examples was the wreckage of Shigenori Nishikaichi's fighter, which he crash-landed on Niihau.^9 You couldn't learn everything by poring over the burned out fragments, but experts could still learn quite a bit about its construction. In July 1942, the Americans recovered a crash-landed Zero on Akutan in the Aleutian Islands that was in good enough shape to be repaired and returned to flying condition by September 1942.^10 If you ever wanted to see a Zero in USN livery, here you go. It was used in tests with American fighters to examine its performance before it was unfortunately destroyed in an accident.
The Zero was indeed a formidable opponent, but not the world-beater that it is sometimes remembered as. It had strengths and weaknesses that could be exploited, same as any aircraft. The American F4F and P-40 were adequate matches for the Zero when employed properly. With the tactics developed in 1941 and 1942, many American fighter pilots could engage the Zero on equal terms. By the time the next generation of American fighter planes arrived, it was no longer a fair fight.
SOURCES
"Dealing with the Japanese Zero," by Capt. John F. O'Connell, USN (Ret.), Air Power History, Vol. 63, No. 3 (FALL 2016), pp. 26-27; https://www.jstor.org/stable/26276773
O'Connell, pp. 25-26
O'Connell, p. 25
A6M2 Zero, National Naval Aviation Museum, https://www.history.navy.mil/content/history/museums/nnam/explore/collections/aircraft/a/a6m2-zero0.html
"The Rise and Fall of The Imperial Japanese Air Forces," by Alvin D. Coox, Aerospace Historian, Vol. 27, No. 2 (SUMMER/JUNE 1980), pp. 80-81; https://www.jstor.org/stable/44523376
O'Connell, p. 26
"Fighter Tactics in WWII," by Lt. Cdr. Dave Persons, USN, Naval Aviation News, July/August 1993, p. 31; https://www.history.navy.mil/content/dam/nhhc/research/histories/naval-aviation/Naval%20Aviation%20News/1990/pdf/ja93.pdf
O'Connell, p. 29
Pieces of a Surviving Zero Tell a Different Pearl Harbor Story, by Nick D'Alto, Air and Space Magazine, July 2007, https://www.airspacemag.com/military-aviation/the-niihau-zero-18029053/?all
Wreckage of A6M2 Zero on Akutan Island, National Naval Aviation Museum; https://www.history.navy.mil/content/history/museums/nnam/explore/collections/aircraft/a/a6m2-zero0/wreckage-of-a6m2-zero-on-akutan-island.html