Historical Background.
Any truly widespread organisation amongst the Aes Sedai collapsed long before the Breaking ended. By the first century AB letters already speak of Forgotten Talents. A number of the smaller groups that formed during the Breaking became permanent, and independent.

In a dictionary from circa 50 AB, ajah, in the Old Tongue, is defined as "an informal and temporary group of people gathered together for a common purpose or goal, or by a common set of beliefs."
Aes Sedai in the AoL were described as as "a vast sea of ajah, all constantly shrinking, growing, dividing, combining, melting away only to be reborn in some new guise and begin the process once more."
However, a dictionary 200 AB (circa) defines Ajah as "a sisterhood of Aes Sedai".

The Decision.
47 AB : the Aes Sedai decide to build a new city.
"Sitting each for her ajah, if they still can be called so as they are, were Elisane Tishar, Mitsora Caal, Karella Fanway, Azille Narof, Saraline Amerano, Dumera Alman, Salindi Casolan, Catlynde Artein, Biranca Hasad, Mailaine Harvole, Nemaira Eldros, Lideine Rajan and several others.
Twelve women not to mention several others.

One wonders at the purposes of the other 'ajahs'.
Also, the description in this chapter makes it seem that the number seven was arrived at by circumstances alone, rather than for some specific reason, as implied by the colours on the Portal Stones.

Decision to build Tar Valon may have been the outcome of the conference the true goal was to unify the Aes Sedai.

White Tower Design.
White Tower building is designed by the Aes Sedai.
500 feet above the ground it is 300 feet wide at the base.
House the Ajah's in the top half, each in its own pie-shaped section.
There seems little doubt that the Aes Sedai intended their numbers to grow, since the Tower and its related buildings were far larger than needed at the time.

I wonder if the present day AS have forgotten this, and if this increases their feeling of low numbers.

Construction.
Construction began in 98AB. It took 104 years of uninterrupted work, until 202AB.
Northharbour and Southharbour were built at this time, though not by Ogier.

OTOH, the books say that they were designed by Ogier, eg. tDR, Chapter 32 begins, "Southharbor itself, the great Ogier-made basin..."

By 98AB the name White Tower had been in use for some time for the planned central structure.

Aes Sedai Structures.
In 98AB Elisane Tishar is the Amyrlin Seat and has been for several years.
A council of seven was recorded as "closely advising the Amyrlin Seat" - these were, Mitsora Caal, Karella Fanway, Azille Narof, Saraline Amerano, Dumera Alman, Salindi Casolan and Kiam Lopiang.

Aftermath.
By the end of the second century AB the seven Ajah's were definitely in existence.
Between roughly 50 and 100AB an extremely vigorous campaign against women "pretending to be Aes Sedai". Letter dated in 77AB, "Lideine and several of her followers were stilled, whereupon the rest submitted themselves and with that example Mailaine ceased her resistance and led her followers to kneel. The rest must be brought to heel."

This of course ties in nicely with the idea that Ny and El were to be treated harshly for such a crime. It seems that the AS loftiness on this one ignores / forgets the fact that the original White Tower Women were practicing a pro-active closed shop policy.

Note :
Library: We are continually told in the series that the TV library is the greatest in the world, and this is despite the destruction during the fourth Trolloc attempt to take Tar Valon during the Trolloc Wars, (circa 1290 AB ) minor damage to the Tower Library in the Great Fire of FY 642, and the somewhat greater damage attributed to arson in FY 993.