Einstein didn't think black holes existed (1916) and it took until 1971 with Cygnus X-1 for serious consideration, which was the smoking gun. 55 years of being

Einstein didn't think black holes existed (1916) and it took until 1971 with Cygnus X-1 for serious consideration, which was the smoking gun. 55 years of being considered probably a math fluke and then observational evidence.