"While most Muggles refuse to believe that magic exists, they find it difficult to account for certain happenings"
-- Professor Phoebus Penrose's report to the Ministry of Magic (DP1)
Ministry of Magic report warning against the dangers of underestimating how much magic Muggles notice (DP1).
Professor Phoebus Penrose headed a committee which produced this report about Muggle suspicions about magic. Among other magical examples, it notes that Muggles have noticed, and had suspicions about, mysterious flying objects, the Loch Ness monster, and crop circles left behind after the Contorting Cereals class of the Annual Wizard Gardening Competition. The report concludes that Muggles are more observant than wizards think (DP1).
While the date printed on DP1 is 31 July 1998, the timeframe for those events is 1992-1993.