Hi Richa,
I think there might be a bit of confusion that I'd like to help clean up. The A4T integration doesn't deal with audience creation. It simply passes the data that used to be sent to Target into Analytics for further analysis.
Creating audiences inside Analytics and passing them into Target to be used in any activity regardless of whether or not it is an A4T activity is part of the People Core Service, specifically, the audiences functionality of the People Core Service.
With that out of the way, any audience created in Analytics as a segment and shared to other solutions in the Experience Cloud is what we call a historical audience. These audiences do have a 24-48 hour delay from the time a visitor qualifies until the visitor becomes actionable within another solution. This is a rolling delay and not a one time setup. This delay is caused because of the way the passing of information works. I wrote a post on this a few months ago that is very much still applicable today. You can have a look ( Why is my historical audience showing as "collecting data"?) here.
As far as other methods, you can possibly do this with profile scripting by incrementing some sort of cookie value for each visit, however, this would require some custom coding on your part. Another option might be real-time audiences via the Audience Library interface. The Audience Library interface creates what we call realtime audiences where the visitor becomes actionable on the next hit or next page. The limitations here are that you are not able to do any sort of a "look back" to see if someone has historically done something. Once you create the audience in Audience Library, there is a one time ~30 min delay to put your ruleset to our edge server and then visitors can qualify in real time.
Without knowing more about your use case, I can't really provide a recommendation as to which method you should use. If you want to provide a bit more information on the use case, I can try to help guide you further. In the meantime, feel free to read through some of our self-help content below:
Documentation
Audience creation options in Adobe Experience Cloud
Adobe Experience Cloud Audiences Community forum
Cheers,
Jantzen