1985-1986, the period of about 18 months after the Amiga came out. You read BYTE magazine from then and it's clear that the magazine (and, more importantly, its readers) viewed the Amiga and the Atari ST as viable, realistic challengers to the Macintosh as leader of mouse-based graphical computing (i.e., anything not IBM/MS-DOS). Neither Commodore nor Atari succeeded in supplanting Apple for reasons I won't get into here.
But you're not asking the right question. Apple itself was having a very difficult time in convincing corporate customers that Macintosh was the answer to anything. Everyone acknowledged that Macintosh's user interface and software were excellent. But DOS was good enough, had a gigantic software library, and by the end of 1986 it was possible to pay $1000 for a PC clone that could run dad's spreadsheets he brought home, and also run Flight Simulator for him and educational games for the kids. The one exception was creative types; desktop publishing and graphic design, with the Laserwriter's PostScript capability, let Apple keep Macintosh alive, while the Apple II line kept bringing in cash even though the PC was eating it and everything else non-DOS alive.
By 1988, although the Commodore 64 still had the largest home computer installed base, the PC was growing so quickly that everyone knew that it would soon take over. Meanwhile, Nintendo was so popular that in one year it sold as the entire C64 installed base since 1982. So every game publisher began shifting to PC and/or consoles. Apple's also huge II installed base also kept it afloat as mentioned above, and the significant educational market let Apple keep producing II models until the early 1990s, almost exactly the same time as when Commodore went bankrupt and discontinued the C64. But realistically, neither the C64 nor the II had been viable markets for software or hardware companies since about 1990.
Apple survived because by the early 1990s Macintosh sales were finally trending upward, with the continuing creative market joined for the first time by substantial home and educational demand thanks to the low-cost Classic and LC models. But the relentless growth and dominance of the PC market, combined with mistakes by Apple in the mid-1990s, caused the company to come within moments of bankruptcy and/or sale in the late 1990s until Steve Jobs came back and pulled off a miracle.