Hare Krishna Nuala Mataji.
When Lord Sri Krishna departed from this planet over five thousand years ago that was the very moment the current age of Kali began.
There is indeed a Golden Age within the age of Kali Yuga, but that age began with Sri Caitanya Mahaprabhu and the advent of His sankirtan movement, and not with the forming of any institution in modern times. There is no monopoly on the sankirtan movement by any institution; the parampara itself retains all rights. Whosoever takes up the sankirtan movement will prosper spiritually, and whosoever deviates from the principles of pure devotion will reap a harvest of mixed results.
We find in the Brahma-vaivarta Purana the mention of a ten thousand year period in which Vaishnavism and the cult of Sri Caitanya will flourish in the world. Afterwards, darkness and ignorance will consume the world.
In the Brahma-vaivarta Purana the Supreme Personality of Godhead, while speaking to Mother Ganges, describes the dawn of the Golden Age by first mentioning those who worship the Lord by mantra. This reference to those who chant mantras as the central focus of their worship indicates Sri Ramanuja and Sri Madhvaite Brahmins.
snanadeva hi jahnavi
"Thereafter by the sight and touch of those who worship me by my mantra, all those sins will be burnt." (Text 51)
Next, the Brahma-vaivarta Purana directly indicates the advent of the Golden Age inaugurated by Sri Caitanya Mahaprabhu with the performance of hari-nama-sankirtan (the chanting holy name) and the recitation of Srimad Bhagavatam.
puranani bhavamti hi
tatra gatva savadhanam
abhih sarddham ca srosyasi
"There will be chanting of the name of Hari and reading of the [Bhagavata] Purana. Reaching such a place, attentively hear." (Text 52)
It is thoroughly indicated that even the most sinful persons will become Vaishnavas by the chanting of the holy names, and due to the presence of such purified Vaishnavas the whole planet will become a place of pilgrimage.
tathapi vaisnava loke
prthivyam yani tirthani
punyanyapi ca jahnavi
"O Ganges, the whole planet will become a pilgrimage site by the presence of Vaisnavas, even though they had been sinful." (Text 55)
Such a blissful condition is then predicted to last ten thousand years.
madbhaktah samti bhu-tale
madbhaktesu gatesu ca
"For 10,000 years of Kali-yuga, such devotees of mine will fill the whole planet. After the departure of my devotees there will only be one varna [outcaste]." (Text 59)
I hope this answered your query. Haribol.