In Satya Yuga Hrinyakashyap thought that Narasimha will never come.

In Treta Yuga, Ravan thought that Ram will never come.

In Dwapar yuga, kansa thought that Krishna will never come.

In Kali Yuga, Kali think that Kalki will never come.

Mllechas can’t trust on the words of Lord because their conscience didn’t allow them but if Dharmic people involve themselves in the same practice then it raises questions on their belief system. The prediction of arrival of Lord always happened before his arrival. If you don’t believe it then you also come in the category of Mllechas because Lord repeated his vow in Bhagwad Gita:

यदा यदा हि धर्मस्य ग्लानिर्भवति भारत।
अभ्युत्थानमधर्मस्य तदाऽऽत्मानं सृजाम्यहम्।।

परित्राणाय साधूनां विनाशाय च दुष्कृताम I
धर्म संस्थापनार्थाय संभवामि युगे युगे II

“Whenever there is a decline in righteousness and an increase in unrighteousness , O Arjun, at that time I manifest myself on earth. To protect the righteous, to annihilate the wicked, and to reestablish the principles of dharma I appear on this earth , age after age.”